यदि \(A=\{1,2,3\}\) और \(B=\{3,4,5\}\) है, तो \(A\cup B\) क्या होगा?
If \(A=\{1,2,3\}\) and \(B=\{3,4,5\}\), what is \(A\cup B\)?
#sets
#union
#easy
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3,4,5} )
B ( {3} )
C ( {1,2} )
D ( {4,5} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5} )
Step 1
Concept
\(A\cup B\) contains all distinct elements of both sets. In exams, write repeated elements only once.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5} ). \(A\cup B\) contains all distinct elements of both sets. In exams, write repeated elements only once.
Step 3
Exam Tip
\(A\cup B\) में दोनों समुच्चयों के सभी अलग-अलग अवयव आते हैं। परीक्षा में दोहराए गए अवयव एक बार ही लिखें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4\}\) है, तो \(A\cap B\) क्या है?
If \(A=\{2,4,6,8\}\) and \(B=\{1,2,3,4\}\), what is \(A\cap B\)?
#sets
#intersection
#easy
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,3} )
B ( {2,4} )
C ( {6,8} )
D ( {1,2,3,4,6,8} )
Explanation opens after your attempt
Correct Answer
B. ( {2,4} )
Step 1
Concept
\(A\cap B\) contains only elements common to both sets. First identify the common elements carefully.
Step 2
Why this answer is correct
The correct answer is B. ( {2,4} ). \(A\cap B\) contains only elements common to both sets. First identify the common elements carefully.
Step 3
Exam Tip
\(A\cap B\) में केवल वे अवयव आते हैं जो दोनों में समान हों। समान अवयव पहचानना सबसे पहला कदम है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{a,b,c,d\}\) और \(B=\{b,d,e\}\) है, तो (A-B) क्या होगा?
If \(A=\{a,b,c,d\}\) and \(B=\{b,d,e\}\), what is (A-B)?
#sets
#difference
#easy
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {a,c} )
B ( {b,d} )
C ( {a,b,c,d,e} )
D ( {e} )
Explanation opens after your attempt
Correct Answer
A. ( {a,c} )
Step 1
Concept
(A-B) contains elements of (A) that are not in (B). While finding difference, remove the common elements from (A).
Step 2
Why this answer is correct
The correct answer is A. ( {a,c} ). (A-B) contains elements of (A) that are not in (B). While finding difference, remove the common elements from (A).
Step 3
Exam Tip
(A-B) में (A) के वे अवयव आते हैं जो (B) में नहीं हैं। अंतर निकालते समय पहले (B) के समान अवयव हटाएं।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{5,10,15\}\) और \(B=\{10,20\}\) है, तो (B-A) क्या है?
If \(A=\{5,10,15\}\) and \(B=\{10,20\}\), what is (B-A)?
#sets
#difference
#order
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {5,15} )
B ( {20} )
C ( {10} )
D ( {5,10,15,20} )
Explanation opens after your attempt
Correct Answer
B. ( {20} )
Step 1
Concept
(B-A) keeps elements of (B) that are not in (A). Remember that (A-B) and (B-A) may be different.
Step 2
Why this answer is correct
The correct answer is B. ( {20} ). (B-A) keeps elements of (B) that are not in (A). Remember that (A-B) and (B-A) may be different.
Step 3
Exam Tip
(B-A) में (B) के वे अवयव रहते हैं जो (A) में नहीं हैं। (A-B) और (B-A) अलग हो सकते हैं।
Login to save your score, XP, coins and progress. Login
\(यदि (A={x:x\) is an even number less than \(10}) और (B={2,3,5,7}) है, तो (A\cap B) क्या है\)?
\(If (A={x:x\) is an even number less than \(10}) and (B={2,3,5,7}), what is (A\cap B)\)?
#sets
#set-builder
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {2} )
B ( {2,4,6,8} )
C ( {3,5,7} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {2} )
Step 1
Concept
Here \(A=\{2,4,6,8\}\), and only (2) is common. Converting set-builder form to roster form helps.
Step 2
Why this answer is correct
The correct answer is A. ( {2} ). Here \(A=\{2,4,6,8\}\), and only (2) is common. Converting set-builder form to roster form helps.
Step 3
Exam Tip
यहां \(A=\{2,4,6,8\}\) है और केवल (2) दोनों में है। पहले समुच्चय को सूची रूप में लिखना उपयोगी है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,3,5,7\}\) और \(B=\{2,4,6,8\}\) है, तो \(A\cap B\) क्या होगा?
If \(A=\{1,3,5,7\}\) and \(B=\{2,4,6,8\}\), what is \(A\cap B\)?
#sets
#disjoint
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3,4,5,6,7,8} )
B ( {1,3,5,7} )
C \( \varnothing \)
D ( {2,4,6,8} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
There is no common element, so the intersection is \( \varnothing \). Disjoint sets always have an empty intersection.
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). There is no common element, so the intersection is \( \varnothing \). Disjoint sets always have an empty intersection.
Step 3
Exam Tip
दोनों समुच्चयों में कोई समान अवयव नहीं है इसलिए प्रतिच्छेद \( \varnothing \) है। असंयुक्त समुच्चयों का प्रतिच्छेद रिक्त होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2\}\) और \(B=\{1,2,3,4\}\) है, तो \(A\cup B\) क्या होगा?
If \(A=\{1,2\}\) and \(B=\{1,2,3,4\}\), what is \(A\cup B\)?
#sets
#union
#subset
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2} )
B ( {3,4} )
C ( {1,2,3,4} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
C. ( {1,2,3,4} )
Step 1
Concept
Since \(A\subseteq B\), \(A\cup B=B\). In subset cases, the larger set is the union.
Step 2
Why this answer is correct
The correct answer is C. ( {1,2,3,4} ). Since \(A\subseteq B\), \(A\cup B=B\). In subset cases, the larger set is the union.
Step 3
Exam Tip
क्योंकि \(A\subseteq B\), इसलिए \(A\cup B=B\) होगा। उपसमुच्चय वाले प्रश्नों में बड़ा समुच्चय संघ होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{p,q\}\) और \(B=\{p,q,r\}\) है, तो \(A\cap B\) क्या है?
If \(A=\{p,q\}\) and \(B=\{p,q,r\}\), what is \(A\cap B\)?
#sets
#intersection
#subset
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {p,q} )
B ( {r} )
C ( {p,q,r} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {p,q} )
Step 1
Concept
All elements of (A) are in (B), so \(A\cap B=A\). In subset cases, the smaller set is the intersection.
Step 2
Why this answer is correct
The correct answer is A. ( {p,q} ). All elements of (A) are in (B), so \(A\cap B=A\). In subset cases, the smaller set is the intersection.
Step 3
Exam Tip
क्योंकि (A) के सभी अवयव (B) में हैं, इसलिए \(A\cap B=A\) है। उपसमुच्चय में प्रतिच्छेद छोटा समुच्चय होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5\}\) और \(B=\{2,4\}\) है, तो (A-B) क्या है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{2,4\}\), what is (A-B)?
#sets
#difference
#easy
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {2,4} )
B ( {1,3,5} )
C ( {1,2,3,4,5} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {1,3,5} )
Step 1
Concept
Removing (2) and (4) from (A) gives ({1,3,5}). Pay attention to the order in set difference.
Step 2
Why this answer is correct
The correct answer is B. ( {1,3,5} ). Removing (2) and (4) from (A) gives ({1,3,5}). Pay attention to the order in set difference.
Step 3
Exam Tip
(A) से (B) के अवयव (2) और (4) हटाने पर ({1,3,5}) बचता है। अंतर में क्रम का ध्यान रखें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{2,3,5,7\}\) और \(B=\{2,3,5,7\}\) है, तो (A-B) क्या होगा?
If \(A=\{2,3,5,7\}\) and \(B=\{2,3,5,7\}\), what is (A-B)?
#sets
#difference
#equalsets
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {2,3,5,7} )
B ( {0} )
C \( \varnothing \)
D ( {2} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
The two sets are equal, so no element of (A) remains. Remember that \(A-A=\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). The two sets are equal, so no element of (A) remains. Remember that \(A-A=\varnothing\).
Step 3
Exam Tip
दोनों समुच्चय समान हैं इसलिए (A) का कोई नया अवयव नहीं बचता। याद रखें \(A-A=\varnothing\) होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{m,n,o\}\) और \(B=\varnothing\) है, तो \(A\cup B\) क्या होगा?
If \(A=\{m,n,o\}\) and \(B=\varnothing\), what is \(A\cup B\)?
#sets
#emptyset
#union
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \( \varnothing \)
B ( {m,n,o} )
C ( {m} )
D ( {n,o} )
Explanation opens after your attempt
Correct Answer
B. ( {m,n,o} )
Step 1
Concept
The empty set has no elements, so \(A\cup \varnothing=A\). Knowing identity rules helps in quick scoring.
Step 2
Why this answer is correct
The correct answer is B. ( {m,n,o} ). The empty set has no elements, so \(A\cup \varnothing=A\). Knowing identity rules helps in quick scoring.
Step 3
Exam Tip
रिक्त समुच्चय में कोई अवयव नहीं होता इसलिए \(A\cup \varnothing=A\) है। पहचान सूत्रों को याद रखना आसान अंक दिलाता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{4,8,12\}\) है, तो \(A\cap \varnothing\) क्या है?
If \(A=\{4,8,12\}\), what is \(A\cap \varnothing\)?
#sets
#emptyset
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {4,8,12} )
B ( {0} )
C \( \varnothing \)
D ( {4} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
Since \(\varnothing\) has no element, there is no common element. Always \(A\cap \varnothing=\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). Since \(\varnothing\) has no element, there is no common element. Always \(A\cap \varnothing=\varnothing\).
Step 3
Exam Tip
\(\varnothing\) में कोई अवयव नहीं है, इसलिए कोई सामान्य अवयव नहीं होगा। हमेशा \(A\cap \varnothing=\varnothing\) होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3\}\) है, तो (A-A) क्या होगा?
If \(A=\{1,2,3\}\), what is (A-A)?
#sets
#difference
#identity
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3} )
B \( \varnothing \)
C ( {0} )
D ( {1} )
Explanation opens after your attempt
Correct Answer
B. \( \varnothing \)
Step 1
Concept
(A-A) asks for elements of (A) not in (A), and none exist. Difference of a set from itself is empty.
Step 2
Why this answer is correct
The correct answer is B. \( \varnothing \). (A-A) asks for elements of (A) not in (A), and none exist. Difference of a set from itself is empty.
Step 3
Exam Tip
(A-A) में (A) के वे अवयव चाहिए जो (A) में नहीं हैं, ऐसा कोई अवयव नहीं है। समान समुच्चय का अंतर रिक्त होता है।
Login to save your score, XP, coins and progress. Login
यदि (n(A)=5), (n(B)=4) और (n\(A\cap B\)=2) है, तो (n\(A\cup B\)) कितना है?
If (n(A)=5), (n(B)=4), and (n\(A\cap B\)=2), what is (n\(A\cup B\))?
#sets
#cardinality
#union
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (7)
B (9)
C (11)
D (3)
Explanation opens after your attempt
Step 1
Concept
Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), the answer is (5+4-2=7). Subtract the common part once.
Step 2
Why this answer is correct
The correct answer is A. (7). Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), the answer is (5+4-2=7). Subtract the common part once.
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) से उत्तर (5+4-2=7) है। सामान्य भाग को एक बार घटाना जरूरी है।
Login to save your score, XP, coins and progress. Login
यदि (n\(A\cup B\)=12), (n(A)=7) और (n(B)=8) है, तो (n\(A\cap B\)) कितना है?
If (n\(A\cup B\)=12), (n(A)=7), and (n(B)=8), what is (n\(A\cap B\))?
#sets
#cardinality
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From the formula, (n\(A\cap B\)=7+8-12=3). Keep signs correct when using the union formula backward.
Step 2
Why this answer is correct
The correct answer is C. (3). From the formula, (n\(A\cap B\)=7+8-12=3). Keep signs correct when using the union formula backward.
Step 3
Exam Tip
सूत्र से (n\(A\cap B\)=7+8-12=3) होगा। संघ वाला सूत्र उल्टा लगाते समय चिन्ह सही रखें।
Login to save your score, XP, coins and progress. Login
यदि (n(A)=10) और (n\(A\cap B\)=4) है, तो (n(A-B)) कितना होगा?
If (n(A)=10) and (n\(A\cap B\)=4), what is (n(A-B))?
#sets
#cardinality
#difference
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (14)
B (10)
C (6)
D (4)
Explanation opens after your attempt
Step 1
Concept
In (A-B), the (4) common elements are removed from (A), so (10-4=6). For difference, count only from the first set.
Step 2
Why this answer is correct
The correct answer is C. (6). In (A-B), the (4) common elements are removed from (A), so (10-4=6). For difference, count only from the first set.
Step 3
Exam Tip
(A-B) में (A) से सामान्य (4) अवयव हटते हैं, इसलिए (10-4=6)। अंतर में केवल पहले समुच्चय की गिनती देखें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{2,4,6\}\) है, तो (B-A) क्या है?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6\}\), what is (B-A)?
#sets
#difference
#subset
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,3,5} )
B ( {2,4,6} )
C \( \varnothing \)
D ( {1,2,3,4,5,6} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
Since \(B\subseteq A\), no element of (B) lies outside (A). Therefore \(B-A=\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). Since \(B\subseteq A\), no element of (B) lies outside (A). Therefore \(B-A=\varnothing\).
Step 3
Exam Tip
क्योंकि \(B\subseteq A\), (B) का कोई अवयव (A) के बाहर नहीं है। इसलिए \(B-A=\varnothing\) है।
Login to save your score, XP, coins and progress. Login
यदि \(A={x:x\in \mathbb{N},x\le 5}\) और \(B=\{3,4,5,6\}\) है, तो \(A\cup B\) क्या है?
If \(A={x:x\in \mathbb{N},x\le 5}\) and \(B=\{3,4,5,6\}\), what is \(A\cup B\)?
#sets
#set-builder
#union
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3,4,5,6} )
B ( {3,4,5} )
C ( {1,2} )
D ( {6} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5,6} )
Step 1
Concept
Here \(A=\{1,2,3,4,5\}\), so the union is ({1,2,3,4,5,6}). List the natural numbers first.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5,6} ). Here \(A=\{1,2,3,4,5\}\), so the union is ({1,2,3,4,5,6}). List the natural numbers first.
Step 3
Exam Tip
यहां \(A=\{1,2,3,4,5\}\) है, इसलिए संघ ({1,2,3,4,5,6}) है। प्राकृतिक संख्याओं को सूचीबद्ध करके हल करें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{0,1,2,3\}\) और \(B=\{2,3,4,5\}\) है, तो (A-B) क्या होगा?
If \(A=\{0,1,2,3\}\) and \(B=\{2,3,4,5\}\), what is (A-B)?
#sets
#difference
#easy
#numerical
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {0,1} )
B ( {4,5} )
C ( {2,3} )
D ( {0,1,2,3,4,5} )
Explanation opens after your attempt
Correct Answer
A. ( {0,1} )
Step 1
Concept
Removing (2) and (3) from (A) leaves ({0,1}). For (A-B), start only with set (A).
Step 2
Why this answer is correct
The correct answer is A. ( {0,1} ). Removing (2) and (3) from (A) leaves ({0,1}). For (A-B), start only with set (A).
Step 3
Exam Tip
(A) में से (B) के अवयव (2) और (3) हटाने पर ({0,1}) बचता है। (A-B) में केवल (A) से शुरू करें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3\}\), \(B=\{3,4\}\) और \(C=\{4,5\}\) है, तो \(A\cup B\cup C\) क्या है?
If \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5\}\), what is \(A\cup B\cup C\)?
#sets
#three-sets
#union
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3,4,5} )
B ( {3,4} )
C ( {1,2,5} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5} )
Step 1
Concept
Taking all distinct elements from the three sets gives ({1,2,3,4,5}). Repetition is not written in a union.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5} ). Taking all distinct elements from the three sets gives ({1,2,3,4,5}). Repetition is not written in a union.
Step 3
Exam Tip
तीनों समुच्चयों के सभी अलग-अलग अवयव लेने पर ({1,2,3,4,5}) मिलता है। संघ में पुनरावृत्ति नहीं लिखी जाती।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4\}\), \(B=\{2,3,5\}\) और \(C=\{3,6\}\) है, तो \(A\cap B\cap C\) क्या है?
If \(A=\{1,2,3,4\}\), \(B=\{2,3,5\}\), and \(C=\{3,6\}\), what is \(A\cap B\cap C\)?
#sets
#three-sets
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {2} )
B ( {3} )
C ( {2,3} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {3} )
Step 1
Concept
The element (3) is in all three sets, so \(A\cap B\cap C={3}\). Check common elements in every set.
Step 2
Why this answer is correct
The correct answer is B. ( {3} ). The element (3) is in all three sets, so \(A\cap B\cap C={3}\). Check common elements in every set.
Step 3
Exam Tip
(3) तीनों समुच्चयों में है, इसलिए \(A\cap B\cap C={3}\) है। तीन समुच्चयों में सामान्य अवयव को सभी में जांचें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4\}\) और \(C=\{5,6\}\) है, तो (A-\(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,4\}\), and \(C=\{5,6\}\), what is (A-\(B\cup C\))?
#sets
#difference
#union
#three-sets
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,3} )
B ( {2,4,5,6} )
C ( {1,2,3,4,5} )
D ( {6} )
Explanation opens after your attempt
Correct Answer
A. ( {1,3} )
Step 1
Concept
\(B\cup C={2,4,5,6}\), and removing these from (A) leaves ({1,3}). Solve the bracket first.
Step 2
Why this answer is correct
The correct answer is A. ( {1,3} ). \(B\cup C={2,4,5,6}\), and removing these from (A) leaves ({1,3}). Solve the bracket first.
Step 3
Exam Tip
\(B\cup C={2,4,5,6}\) है और (A) से इन्हें हटाने पर ({1,3}) बचता है। पहले कोष्ठक हल करें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{a,b,c,d\}\), \(B=\{b,c,e\}\) और \(C=\{c,d,e\}\) है, तो (A\cap \(B\cup C\)) क्या है?
If \(A=\{a,b,c,d\}\), \(B=\{b,c,e\}\), and \(C=\{c,d,e\}\), what is (A\cap \(B\cup C\))?
#sets
#union
#intersection
#three-sets
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {b,c,d} )
B ( {a} )
C ( {e} )
D ( {a,b,c,d,e} )
Explanation opens after your attempt
Correct Answer
A. ( {b,c,d} )
Step 1
Concept
\(B\cup C={b,c,d,e}\), and its common part with (A) is ({b,c,d}). Solve combined operations step by step.
Step 2
Why this answer is correct
The correct answer is A. ( {b,c,d} ). \(B\cup C={b,c,d,e}\), and its common part with (A) is ({b,c,d}). Solve combined operations step by step.
Step 3
Exam Tip
\(B\cup C={b,c,d,e}\) है और (A) से इसका सामान्य भाग ({b,c,d}) है। संयुक्त क्रियाओं में क्रम से हल करें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4\}\), \(B=\{3,4,5\}\) और \(C=\{4,5,6\}\) है, तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{1,2,3,4\}\), \(B=\{3,4,5\}\), and \(C=\{4,5,6\}\), what is (\(A\cap B\)\cup C)?
#sets
#intersection
#union
#three-sets
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {3,4,5,6} )
B ( {4} )
C ( {1,2,3,4,5,6} )
D ( {3,4} )
Explanation opens after your attempt
Correct Answer
A. ( {3,4,5,6} )
Step 1
Concept
\(A\cap B={3,4}\), and its union with (C) gives ({3,4,5,6}). Do the bracket first.
Step 2
Why this answer is correct
The correct answer is A. ( {3,4,5,6} ). \(A\cap B={3,4}\), and its union with (C) gives ({3,4,5,6}). Do the bracket first.
Step 3
Exam Tip
\(A\cap B={3,4}\) है, फिर इसे (C) से मिलाने पर ({3,4,5,6}) मिलता है। कोष्ठक पहले करें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,3,5\}\) और \(B=\{1,2,3,4,5\}\) है, तो (B-A) क्या है?
If \(A=\{1,3,5\}\) and \(B=\{1,2,3,4,5\}\), what is (B-A)?
#sets
#difference
#subset
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,3,5} )
B ( {2,4} )
C ( {1,2,3,4,5} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {2,4} )
Step 1
Concept
Removing (1,3,5) from (B) leaves ({2,4}). For (B-A), start with (B).
Step 2
Why this answer is correct
The correct answer is B. ( {2,4} ). Removing (1,3,5) from (B) leaves ({2,4}). For (B-A), start with (B).
Step 3
Exam Tip
(B) से (A) के अवयव (1,3,5) हटाने पर ({2,4}) बचता है। (B-A) में शुरुआत (B) से करें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{2,4,6,8,10\}\) और \(B=\{1,2,3,4,5\}\) है, तो \(A\cup B\) में कितने अवयव हैं?
If \(A=\{2,4,6,8,10\}\) and \(B=\{1,2,3,4,5\}\), how many elements are in \(A\cup B\)?
#sets
#cardinality
#union
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (5)
B (7)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4,5,6,8,10}\), so it has (8) elements. Do not count common elements twice.
Step 2
Why this answer is correct
The correct answer is C. (8). \(A\cup B={1,2,3,4,5,6,8,10}\), so it has (8) elements. Do not count common elements twice.
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6,8,10}\) है, इसलिए अवयव (8) हैं। गिनते समय समान अवयव दो बार न गिनें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{10,20,30,40\}\) और \(B=\{20,40,60\}\) है, तो \(A\cap B\) में कितने अवयव हैं?
If \(A=\{10,20,30,40\}\) and \(B=\{20,40,60\}\), how many elements are in \(A\cap B\)?
#sets
#cardinality
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The common elements are (20) and (40), so the number is (2). In intersection, count only common elements.
Step 2
Why this answer is correct
The correct answer is B. (2). The common elements are (20) and (40), so the number is (2). In intersection, count only common elements.
Step 3
Exam Tip
सामान्य अवयव (20) और (40) हैं, इसलिए संख्या (2) है। प्रतिच्छेद में केवल समान अवयव गिने जाते हैं।
Login to save your score, XP, coins and progress. Login
\(यदि (A={x:x\) is a vowel in English alphabet\(}) और (B={a,e,i}) है, तो (A-B) क्या है\)?
\(If (A={x:x\) is a vowel in English alphabet\(}) and (B={a,e,i}), what is (A-B)\)?
#sets
#difference
#roster
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {o,u} )
B ( {a,e,i} )
C ( {a,e,i,o,u} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {o,u} )
Step 1
Concept
\(A=\{a,e,i,o,u\}\), and removing (B) leaves ({o,u}). First convert the descriptive set into roster form.
Step 2
Why this answer is correct
The correct answer is A. ( {o,u} ). \(A=\{a,e,i,o,u\}\), and removing (B) leaves ({o,u}). First convert the descriptive set into roster form.
Step 3
Exam Tip
\(A=\{a,e,i,o,u\}\) है और (B) हटाने पर ({o,u}) बचता है। पहले वर्णनात्मक समुच्चय को सूची रूप में बदलें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{2,4,6\}\) और \(B=\{6,8,10\}\) है, तो \(A\cup B\) में कौन सा अवयव अवश्य होगा?
If \(A=\{2,4,6\}\) and \(B=\{6,8,10\}\), which element must belong to \(A\cup B\)?
#sets
#union
#membership
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B (8)
C (12)
D (1)
Explanation opens after your attempt
Step 1
Concept
(8) is in set (B), so it is also in \(A\cup B\). A union includes elements from either set.
Step 2
Why this answer is correct
The correct answer is B. (8). (8) is in set (B), so it is also in \(A\cup B\). A union includes elements from either set.
Step 3
Exam Tip
(8) समुच्चय (B) में है, इसलिए वह \(A\cup B\) में भी होगा। संघ में किसी भी एक समुच्चय का अवयव शामिल होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4\}\) और \(B=\{2,4,6,8\}\) है, तो कौन सा अवयव (A-B) में है?
If \(A=\{1,2,3,4\}\) and \(B=\{2,4,6,8\}\), which element is in (A-B)?
#sets
#difference
#membership
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (4)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
(3) is in (A) but not in (B), so \(3\in A-B\). In difference, keep elements of the first set not in the second.
Step 2
Why this answer is correct
The correct answer is C. (3). (3) is in (A) but not in (B), so \(3\in A-B\). In difference, keep elements of the first set not in the second.
Step 3
Exam Tip
(3) (A) में है लेकिन (B) में नहीं है, इसलिए \(3\in A-B\) है। अंतर में केवल पहले समुच्चय के बाहर वाले सामान्य अवयव हटते हैं।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{red,blue\}\) और \(B=\{blue,green\}\) है, तो \(A\cap B\) क्या है?
If \(A=\{red,blue\}\) and \(B=\{blue,green\}\), what is \(A\cap B\)?
#sets
#intersection
#word-set
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {red} )
B ( {blue} )
C ( {green} )
D ( {red,blue,green} )
Explanation opens after your attempt
Correct Answer
B. ( {blue} )
Step 1
Concept
Only (blue) is common to both sets. Write only common elements in the intersection.
Step 2
Why this answer is correct
The correct answer is B. ( {blue} ). Only (blue) is common to both sets. Write only common elements in the intersection.
Step 3
Exam Tip
दोनों समुच्चयों में केवल (blue) समान है। प्रतिच्छेद में सिर्फ समान अवयव लिखें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{cat,dog,cow\}\) और \(B=\{dog,goat\}\) है, तो \(A\cup B\) क्या होगा?
If \(A=\{cat,dog,cow\}\) and \(B=\{dog,goat\}\), what is \(A\cup B\)?
#sets
#union
#word-set
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {cat,dog,cow,goat} )
B ( {dog} )
C ( {cat,cow} )
D ( {goat} )
Explanation opens after your attempt
Correct Answer
A. ( {cat,dog,cow,goat} )
Step 1
Concept
The union contains all distinct names, so it is ({cat,dog,cow,goat}). Write the repeated name (dog) only once.
Step 2
Why this answer is correct
The correct answer is A. ( {cat,dog,cow,goat} ). The union contains all distinct names, so it is ({cat,dog,cow,goat}). Write the repeated name (dog) only once.
Step 3
Exam Tip
संघ में सभी अलग-अलग नाम आते हैं, इसलिए ({cat,dog,cow,goat}) है। समान नाम (dog) को एक बार लिखें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,4,9,16\}\) और \(B=\{4,16,25\}\) है, तो (A-B) क्या है?
If \(A=\{1,4,9,16\}\) and \(B=\{4,16,25\}\), what is (A-B)?
#sets
#difference
#squares
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,9} )
B ( {4,16} )
C ( {25} )
D ( {1,4,9,16,25} )
Explanation opens after your attempt
Correct Answer
A. ( {1,9} )
Step 1
Concept
The elements (4) and (16) of (A) are also in (B), so they are removed. The remaining elements are ({1,9}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,9} ). The elements (4) and (16) of (A) are also in (B), so they are removed. The remaining elements are ({1,9}).
Step 3
Exam Tip
(A) के (4) और (16) (B) में भी हैं, इसलिए हटते हैं। बचे अवयव ({1,9}) हैं।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{0,2,4,6\}\) और \(B=\{1,3,5\}\) है, तो (A-B) क्या होगा?
If \(A=\{0,2,4,6\}\) and \(B=\{1,3,5\}\), what is (A-B)?
#sets
#difference
#disjoint
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \( \varnothing \)
B ( {0,2,4,6} )
C ( {1,3,5} )
D ( {0,1,2,3,4,5,6} )
Explanation opens after your attempt
Correct Answer
B. ( {0,2,4,6} )
Step 1
Concept
The sets are disjoint, so nothing is removed from (A). For disjoint sets, (A-B=A).
Step 2
Why this answer is correct
The correct answer is B. ( {0,2,4,6} ). The sets are disjoint, so nothing is removed from (A). For disjoint sets, (A-B=A).
Step 3
Exam Tip
दोनों समुच्चय असंयुक्त हैं, इसलिए (A) से कुछ नहीं हटेगा। असंयुक्त होने पर (A-B=A) होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3\}\) और \(B=\{4,5\}\) है, तो \(A\cup B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{4,5\}\), what is \(A\cup B\)?
#sets
#union
#disjoint
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3,4,5} )
B \( \varnothing \)
C ( {1,2,3} )
D ( {4,5} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5} )
Step 1
Concept
The union of disjoint sets contains all elements of both sets. Here the answer is ({1,2,3,4,5}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5} ). The union of disjoint sets contains all elements of both sets. Here the answer is ({1,2,3,4,5}).
Step 3
Exam Tip
असंयुक्त समुच्चयों का संघ भी दोनों के सभी अवयवों का समुच्चय होता है। यहां उत्तर ({1,2,3,4,5}) है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{2,3,4,5\}\) और \(B=\{4,5,6,7\}\) है, तो \((A-B)\cup(B-A)\) क्या है?
If \(A=\{2,3,4,5\}\) and \(B=\{4,5,6,7\}\), what is \((A-B)\cup(B-A)\)?
#sets
#symmetric-difference
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {2,3,6,7} )
B ( {4,5} )
C ( {2,3,4,5,6,7} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {2,3,6,7} )
Step 1
Concept
(A-B={2,3}) and (B-A={6,7}), so the union is ({2,3,6,7}). This is the union of non-common parts.
Step 2
Why this answer is correct
The correct answer is A. ( {2,3,6,7} ). (A-B={2,3}) and (B-A={6,7}), so the union is ({2,3,6,7}). This is the union of non-common parts.
Step 3
Exam Tip
(A-B={2,3}) और (B-A={6,7}) है, इसलिए संघ ({2,3,6,7}) है। यह सामान्य भाग हटाकर बचे भागों का संघ है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\) है, तो (\(A\cup B\)-A) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is (\(A\cup B\)-A)?
#sets
#union
#difference
#identity
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2} )
B ( {5,6} )
C ( {3,4} )
D ( {1,2,3,4,5,6} )
Explanation opens after your attempt
Correct Answer
B. ( {5,6} )
Step 1
Concept
\(A\cup B={1,2,3,4,5,6}\), and removing (A) leaves ({5,6}). This is equal to (B-A).
Step 2
Why this answer is correct
The correct answer is B. ( {5,6} ). \(A\cup B={1,2,3,4,5,6}\), and removing (A) leaves ({5,6}). This is equal to (B-A).
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6}\) है और (A) हटाने पर ({5,6}) बचता है। यह (B-A) के बराबर है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{a,b,c\}\) और \(B=\{c,d,e\}\) है, तो (\(A\cup B\)-B) क्या है?
If \(A=\{a,b,c\}\) and \(B=\{c,d,e\}\), what is (\(A\cup B\)-B)?
#sets
#union
#difference
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {a,b} )
B ( {c} )
C ( {d,e} )
D ( {a,b,c,d,e} )
Explanation opens after your attempt
Correct Answer
A. ( {a,b} )
Step 1
Concept
The union is ({a,b,c,d,e}), and removing (B) leaves ({a,b}). This gives the same result as (A-B).
Step 2
Why this answer is correct
The correct answer is A. ( {a,b} ). The union is ({a,b,c,d,e}), and removing (B) leaves ({a,b}). This gives the same result as (A-B).
Step 3
Exam Tip
संघ ({a,b,c,d,e}) है और (B) हटाने पर ({a,b}) बचता है। यह (A-B) जैसा परिणाम देता है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5\}\) और \(B=\{2,4,6\}\) है, तो \(A\cap (A-B)\) क्या है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{2,4,6\}\), what is \(A\cap (A-B)\)?
#sets
#difference
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,3,5} )
B ( {2,4} )
C ( {6} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,3,5} )
Step 1
Concept
First (A-B={1,3,5}), and it is already a part of (A). Therefore the intersection is ({1,3,5}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,3,5} ). First (A-B={1,3,5}), and it is already a part of (A). Therefore the intersection is ({1,3,5}).
Step 3
Exam Tip
पहले (A-B={1,3,5}) है और यह (A) का ही भाग है। इसलिए प्रतिच्छेद ({1,3,5}) है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3\}\) और \(B=\{2,3,4\}\) है, तो (A\cap \(A\cup B\)) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{2,3,4\}\), what is (A\cap \(A\cup B\))?
#sets
#absorption
#intersection
#union
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3} )
B ( {2,3} )
C ( {1,2,3,4} )
D ( {4} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
\(A\cup B\) contains all elements of (A), so (A\cap \(A\cup B\)=A). This is called the absorption law.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). \(A\cup B\) contains all elements of (A), so (A\cap \(A\cup B\)=A). This is called the absorption law.
Step 3
Exam Tip
\(A\cup B\) में (A) के सभी अवयव हैं, इसलिए (A\cap \(A\cup B\)=A) है। इसे अवशोषण नियम कहते हैं।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{2,4\}\) और \(B=\{4,6,8\}\) है, तो (A\cup \(A\cap B\)) क्या है?
If \(A=\{2,4\}\) and \(B=\{4,6,8\}\), what is (A\cup \(A\cap B\))?
#sets
#absorption
#union
#intersection
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {4} )
B ( {2,4} )
C ( {2,4,6,8} )
D ( {6,8} )
Explanation opens after your attempt
Correct Answer
B. ( {2,4} )
Step 1
Concept
\(A\cap B={4}\), and \(A\cup {4}=A\). This is also an example of the absorption law.
Step 2
Why this answer is correct
The correct answer is B. ( {2,4} ). \(A\cap B={4}\), and \(A\cup {4}=A\). This is also an example of the absorption law.
Step 3
Exam Tip
\(A\cap B={4}\) है और \(A\cup {4}=A\) होगा। यह भी अवशोषण नियम का उदाहरण है।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\) और \(C=\{1,2,3\}\) है, तो (B-C) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), and \(C=\{1,2,3\}\), what is (B-C)?
#sets
#difference
#three-sets
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {4,6} )
B ( {1,3} )
C ( {2} )
D ( {1,2,3,4,6} )
Explanation opens after your attempt
Correct Answer
A. ( {4,6} )
Step 1
Concept
The common element (2) is removed from (B), so ({4,6}) remains. Even with three sets, focus on the asked operation.
Step 2
Why this answer is correct
The correct answer is A. ( {4,6} ). The common element (2) is removed from (B), so ({4,6}) remains. Even with three sets, focus on the asked operation.
Step 3
Exam Tip
(B) में से (C) का समान अवयव (2) हटता है, इसलिए ({4,6}) बचता है। तीसरा समुच्चय होने पर भी चुनी गई क्रिया पर ध्यान दें।
Login to save your score, XP, coins and progress. Login
एक कक्षा में (18) विद्यार्थी क्रिकेट खेलते हैं, (12) फुटबॉल खेलते हैं और (5) दोनों खेलते हैं। कम से कम एक खेल खेलने वाले विद्यार्थियों की संख्या क्या है?
In a class, (18) students play cricket, (12) play football, and (5) play both. How many students play at least one game?
#sets
#word-problem
#union
#cardinality
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (25)
B (30)
C (35)
D (11)
Explanation opens after your attempt
Step 1
Concept
At least one game means (n\(A\cup B\)=18+12-5=25). Subtract those who play both to avoid double counting.
Step 2
Why this answer is correct
The correct answer is A. (25). At least one game means (n\(A\cup B\)=18+12-5=25). Subtract those who play both to avoid double counting.
Step 3
Exam Tip
कम से कम एक खेल (n\(A\cup B\)=18+12-5=25) होगा। दोनों खेलने वालों को दो बार गिनने से बचने के लिए घटाएं।
Login to save your score, XP, coins and progress. Login
एक समूह में (20) विद्यार्थी गणित पसंद करते हैं, (15) विज्ञान पसंद करते हैं और (8) दोनों पसंद करते हैं। केवल गणित पसंद करने वाले कितने हैं?
In a group, (20) students like Mathematics, (15) like Science, and (8) like both. How many like only Mathematics?
#sets
#word-problem
#difference
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (12)
B (7)
C (27)
D (35)
Explanation opens after your attempt
Step 1
Concept
Only Mathematics is (20-8=12). For only-type questions, subtract the common part from the related set.
Step 2
Why this answer is correct
The correct answer is A. (12). Only Mathematics is (20-8=12). For only-type questions, subtract the common part from the related set.
Step 3
Exam Tip
केवल गणित (=20-8=12) है। केवल वाले प्रश्न में संबंधित समुच्चय से सामान्य भाग घटाएं।
Login to save your score, XP, coins and progress. Login
यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5\}\) और \(B=\{2,3,4\}\) है, तो \(A\cup B\) क्या है?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5\}\), and \(B=\{2,3,4\}\), what is \(A\cup B\)?
#sets
#universal-set
#union
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {1,2,3,4,5} )
B ( {6,7} )
C ( {3} )
D ( {1,2,3,4,5,6,7} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5} )
Step 1
Concept
\(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5} ). \(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).
Step 3
Exam Tip
\(A\cup B\) में (A) और (B) के सभी अलग-अलग अवयव आते हैं। (U) केवल संदर्भ समुच्चय है, हर बार पूरा (U) उत्तर नहीं होता।
Login to save your score, XP, coins and progress. Login
यदि \(U=\{a,b,c,d,e\}\), \(A=\{a,b,d\}\) और \(B=\{b,c\}\) है, तो (A-B) क्या है?
If \(U=\{a,b,c,d,e\}\), \(A=\{a,b,d\}\), and \(B=\{b,c\}\), what is (A-B)?
#sets
#universal-set
#difference
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {a,d} )
B ( {b} )
C ( {c,e} )
D ( {a,b,c,d,e} )
Explanation opens after your attempt
Correct Answer
A. ( {a,d} )
Step 1
Concept
The common element (b) is removed from (A), leaving ({a,d}). Even when a universal set is given, find the difference only between the asked sets.
Step 2
Why this answer is correct
The correct answer is A. ( {a,d} ). The common element (b) is removed from (A), leaving ({a,d}). Even when a universal set is given, find the difference only between the asked sets.
Step 3
Exam Tip
(A) से (B) का समान अवयव (b) हटता है और ({a,d}) बचता है। सार्वत्रिक समुच्चय दिए होने पर भी अंतर केवल दिए गए दो समुच्चयों से निकालें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{1,2,3,4,5\}\), \(B=\{3,4,5,6\}\) और \(C=\{5,6,7\}\) है, तो \(A\cap(B-C)\) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{3,4,5,6\}\), and \(C=\{5,6,7\}\), what is \(A\cap(B-C)\)?
#sets
#difference
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {3,4} )
B ( {5} )
C ( {3,4,5} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {3,4} )
Step 1
Concept
First (B-C={3,4}), then the common part with (A) is ({3,4}). Always solve the operation inside brackets first.
Step 2
Why this answer is correct
The correct answer is A. ( {3,4} ). First (B-C={3,4}), then the common part with (A) is ({3,4}). Always solve the operation inside brackets first.
Step 3
Exam Tip
पहले (B-C={3,4}) है, फिर (A) के साथ सामान्य भाग ({3,4}) मिलता है। कोष्ठक वाली क्रिया हमेशा पहले करें।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{2,5,8,11\}\) और \(B=\{1,5,9,11\}\) है, तो (\(A\cup B\)-\(A\cap B\)) क्या है?
If \(A=\{2,5,8,11\}\) and \(B=\{1,5,9,11\}\), what is (\(A\cup B\)-\(A\cap B\))?
#sets
#union
#intersection
#difference
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ( {5,11} )
B ( {1,2,8,9} )
C ( {1,2,5,8,9,11} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {1,2,8,9} )
Step 1
Concept
Removing the common elements (5) and (11) from the union leaves ({1,2,8,9}). This gives the non-common parts.
Step 2
Why this answer is correct
The correct answer is B. ( {1,2,8,9} ). Removing the common elements (5) and (11) from the union leaves ({1,2,8,9}). This gives the non-common parts.
Step 3
Exam Tip
संघ से समान भाग (5) और (11) हटाने पर ({1,2,8,9}) बचता है। यह सामान्य भाग को हटाकर अलग-अलग भाग देता है।
Login to save your score, XP, coins and progress. Login
यदि (n(A)=16), (n(B)=13) और (n\(A\cup B\)=21) है, तो (n\(A\cap B\)) कितना है?
If (n(A)=16), (n(B)=13), and (n\(A\cup B\)=21), what is (n\(A\cap B\))?
#sets
#cardinality
#intersection
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Using the formula, (n\(A\cap B\)=16+13-21=8). The common part is counted twice in the union formula, so it is subtracted.
Step 2
Why this answer is correct
The correct answer is C. (8). Using the formula, (n\(A\cap B\)=16+13-21=8). The common part is counted twice in the union formula, so it is subtracted.
Step 3
Exam Tip
सूत्र से (n\(A\cap B\)=16+13-21=8) होगा। संघ के सूत्र में सामान्य भाग दो बार गिना जाता है, इसलिए उसे घटाया जाता है।
Login to save your score, XP, coins and progress. Login
एक सर्वे में (24) विद्यार्थियों ने हिंदी चुनी, (18) विद्यार्थियों ने अंग्रेजी चुनी और (10) विद्यार्थियों ने दोनों चुनी। केवल अंग्रेजी चुनने वाले कितने विद्यार्थी हैं?
In a survey, (24) students chose Hindi, (18) students chose English, and (10) students chose both. How many students chose only English?
#sets
#word-problem
#difference
#easy
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (8)
B (10)
C (18)
D (32)
Explanation opens after your attempt
Step 1
Concept
Only English is (18-10=8). In only-type questions, subtract the intersection from that set.
Step 2
Why this answer is correct
The correct answer is A. (8). Only English is (18-10=8). In only-type questions, subtract the intersection from that set.
Step 3
Exam Tip
केवल अंग्रेजी (=18-10=8) है। केवल वाले प्रश्न में उस समुच्चय से प्रतिच्छेद घटाएं।
Login to save your score, XP, coins and progress. Login
