13 results found for "complements" in all classes.
यदि \(A\subseteq B\), तो पूरकों के बारे में कौन सा संबंध सही है?
If \(A\subseteq B\), which relation about complements is correct?
#sets
#subset
#complement-property
A \(A^{c}\subseteq B^{c}\)
B \(B^{c}\subseteq A^{c}\)
C \(A^{c}=B^{c}\)
D \(A^{c}\cap B^{c}=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(B^{c}\subseteq A^{c}\)
Step 1
Concept
When the set becomes larger, its complement becomes smaller, so \(B^{c}\subseteq A^{c}\). Complements reverse the subset order.
Step 2
Why this answer is correct
The correct answer is B. \(B^{c}\subseteq A^{c}\). When the set becomes larger, its complement becomes smaller, so \(B^{c}\subseteq A^{c}\). Complements reverse the subset order.
Step 3
Exam Tip
बड़ा समुच्चय लेने पर पूरक छोटा हो जाता है, इसलिए \(B^{c}\subseteq A^{c}\)। उपसमुच्चय में पूरक का क्रम उलट जाता है।
Login to save your score, XP, coins and progress. Login
यदि \(A\subseteq B\subseteq C\subseteq U\) है, तो पूरकों के लिए कौन सा संबंध सही है?
If \(A\subseteq B\subseteq C\subseteq U\), which relation is correct for complements?
#sets
#complement
#subset_property
A \(C^c\subseteq B^c\subseteq A^c\)
B \(A^c\subseteq B^c\subseteq C^c\)
C \(A^c=B^c=C^c\)
D \(A^c\cap C^c=U\)
Explanation opens after your attempt
Correct Answer
A. \(C^c\subseteq B^c\subseteq A^c\)
Step 1
Concept
The order of inclusion reverses after taking complements. Hence the complement of the largest set (C) is the smallest.
Step 2
Why this answer is correct
The correct answer is A. \(C^c\subseteq B^c\subseteq A^c\). The order of inclusion reverses after taking complements. Hence the complement of the largest set (C) is the smallest.
Step 3
Exam Tip
पूरक लेने पर समावेशन का क्रम उलट जाता है। इसलिए सबसे बड़े (C) का पूरक सबसे छोटा होगा।
Login to save your score, XP, coins and progress. Login
यदि \(A\subseteq B\) है, तो पूरकों के लिए कौन सा संबंध सही है?
If \(A\subseteq B\), which relation is correct for the complements?
#sets
#complement
#subset_property
A \(B^c\subseteq A^c\)
B \(A^c\subseteq B^c\)
C \(A^c=B^c\)
D \(A^c\cap B^c=U\)
Explanation opens after your attempt
Correct Answer
A. \(B^c\subseteq A^c\)
Step 1
Concept
The complement of the larger set is smaller, so the order reverses. From \(A\subseteq B\), we get \(B^c\subseteq A^c\).
Step 2
Why this answer is correct
The correct answer is A. \(B^c\subseteq A^c\). The complement of the larger set is smaller, so the order reverses. From \(A\subseteq B\), we get \(B^c\subseteq A^c\).
Step 3
Exam Tip
बड़े समुच्चय का पूरक छोटा होता है, इसलिए क्रम उलट जाता है। \(A\subseteq B\) से \(B^c\subseteq A^c\) मिलता है।
Login to save your score, XP, coins and progress. Login
यदि \(A\subseteq B\subseteq U\) है, तो पूरकों के लिए कौन सा संबंध सही है?
If \(A\subseteq B\subseteq U\), which relation is correct for complements?
#sets
#complement
#subset relation
#class 11
A \(A'\subseteq B'\)
B \(B'\subseteq A'\)
C (A'=B')
D \(A'\cap B'=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(B'\subseteq A'\)
Step 1
Concept
The complement of the smaller set is larger. If \(A\subseteq B\), then \(B'\subseteq A'\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(B'\subseteq A'\). The complement of the smaller set is larger. If \(A\subseteq B\), then \(B'\subseteq A'\) is correct.
Step 3
Exam Tip
छोटे समुच्चय का पूरक बड़ा होता है। \(A\subseteq B\) होने पर \(B'\subseteq A'\) सही है।
Login to save your score, XP, coins and progress. Login
यदि \(A\subseteq U\), \(B\subseteq U\), और \(A\subseteq B\) है, तो पूरकों के लिए कौन सा संबंध सही है?
If \(A\subseteq U\), \(B\subseteq U\), and \(A\subseteq B\), which relation is correct for complements?
#sets
#complement
#subset relation
#class 11
A \(A'\subseteq B'\)
B \(B'\subseteq A'\)
C (A'=B')
D \(A'\cap B'=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(B'\subseteq A'\)
Step 1
Concept
If \(A\subseteq B\), then every element outside (B) is also outside (A). Hence \(B'\subseteq A'\).
Step 2
Why this answer is correct
The correct answer is B. \(B'\subseteq A'\). If \(A\subseteq B\), then every element outside (B) is also outside (A). Hence \(B'\subseteq A'\).
Step 3
Exam Tip
यदि \(A\subseteq B\) है, तो (B) के बाहर के तत्व (A) के बाहर भी होंगे। इसलिए \(B'\subseteq A'\) होता है।
Login to save your score, XP, coins and progress. Login
यदि \(A\subseteq B\) है, तो पूरकों के लिए कौन सा कथन सही है?
If \(A\subseteq B\), which statement about complements is correct?
#subsets
#complement
#logic
A \(B^c\subseteq A^c\)
B \(A^c\subseteq B^c\)
C \(A^c=B^c\) हमेशा / \(A^c=B^c\) always
D \(A^c\cap B^c=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(B^c\subseteq A^c\)
Step 1
Concept
The complement of the larger set is smaller. The subset relation reverses under complements.
Step 2
Why this answer is correct
The correct answer is A. \(B^c\subseteq A^c\). The complement of the larger set is smaller. The subset relation reverses under complements.
Step 3
Exam Tip
बड़े समुच्चय का पूरक छोटा होता है। उपसमुच्चय संबंध पूरक लेने पर उलट जाता है।
Login to save your score, XP, coins and progress. Login
यदि \(U=\mathbb{R}\), (A=\(-\infty,2]\) और \(B=[-1,\infty\)), तो \(A'\cap B'\) क्या है?
If \(U=\mathbb{R}\), (A=\(-\infty,2]\), and \(B=[-1,\infty\)), what is \(A'\cap B'\)?
#sets
#intervals
#intersection-of-complements
#empty-set
A \(\varnothing\)
B ((-1,2])
C (\(2,\infty\))
D (\(-\infty,-1\))
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
(A'=\(2,\infty\)) and (B'=\(-\infty,-1\)). They have no common real element.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). (A'=\(2,\infty\)) and (B'=\(-\infty,-1\)). They have no common real element.
Step 3
Exam Tip
(A'=\(2,\infty\)) और (B'=\(-\infty,-1\)) हैं। इनका कोई समान वास्तविक सदस्य नहीं है।
Login to save your score, XP, coins and progress. Login
यदि \(U={1,2,\ldots,100}\), \(A={x:x\in U,10\mid x}\) और \(B={x:x\in U,15\mid x}\), तो (n\(A'\cup B'\)) क्या है?
If \(U={1,2,\ldots,100}\), \(A={x:x\in U,10\mid x}\), and \(B={x:x\in U,15\mid x}\), what is (n\(A'\cup B'\))?
#sets
#de-morgan
#union-of-complements
#counting
A (97)
B (3)
C (90)
D (94)
Explanation opens after your attempt
Step 1
Concept
(A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (30), so the complement is (100-3=97).
Step 2
Why this answer is correct
The correct answer is A. (97). (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (30), so the complement is (100-3=97).
Step 3
Exam Tip
(A'\cup B'=\(A\cap B\)') है। \(A\cap B\) में (30) के (3) गुणज हैं, इसलिए पूरक (100-3=97) है।
Login to save your score, XP, coins and progress. Login
यदि \(U=\mathbb{R}\), \(A=[1,\infty\)) और (B=\(-\infty,4\)), तो \(A'\cup B'\) क्या है?
If \(U=\mathbb{R}\), \(A=[1,\infty\)), and (B=\(-\infty,4\)), what is \(A'\cup B'\)?
#sets
#intervals
#union-of-complements
#real-line
A (\(-\infty,1\)\cup[4,\infty))
B ([1,4))
C ((-\infty,1]\cup\(4,\infty\))
D ((1,4])
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,1\)\cup[4,\infty))
Step 1
Concept
(A'=\(-\infty,1\)) and \(B'=[4,\infty\)). Their union is (\(-\infty,1\)\cup[4,\infty)).
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,1\)\cup[4,\infty)). (A'=\(-\infty,1\)) and \(B'=[4,\infty\)). Their union is (\(-\infty,1\)\cup[4,\infty)).
Step 3
Exam Tip
(A'=\(-\infty,1\)) और \(B'=[4,\infty\)) हैं। उनका संघ (\(-\infty,1\)\cup[4,\infty)) है।
Login to save your score, XP, coins and progress. Login
यदि \(U={1,2,\ldots,45}\), \(A={x:x \in U,3\mid x}\), \(B={x:x \in U,5\mid x}\), तो (n\(A'\cup B'\)) क्या है?
If \(U={1,2,\ldots,45}\), \(A={x:x \in U,3\mid x}\), \(B={x:x \in U,5\mid x}\), what is (n\(A'\cup B'\))?
#sets
#de-morgan
#union-of-complements
#counting
A (42)
B (3)
C (33)
D (30)
Explanation opens after your attempt
Step 1
Concept
By De Morgan, (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (15), so the complement has (45-3=42) elements.
Step 2
Why this answer is correct
The correct answer is A. (42). By De Morgan, (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (15), so the complement has (45-3=42) elements.
Step 3
Exam Tip
डी मॉर्गन से (A'\cup B'=\(A\cap B\)') है। \(A\cap B\) में (15) के (3) गुणज हैं, इसलिए पूरक (45-3=42) है।
Login to save your score, XP, coins and progress. Login
यदि \(U=\mathbb{R}\), (A=\(-\infty,0]\) और \(B=[2,\infty\)), तो \(A' \cap B'\) क्या है?
If \(U=\mathbb{R}\), (A=\(-\infty,0]\), and \(B=[2,\infty\)), what is \(A' \cap B'\)?
#sets
#intervals
#intersection-of-complements
#de-morgan
A ((0,2))
B ([0,2])
C (\(-\infty,0] \cup [2,\infty\))
D (\(0,\infty\))
Explanation opens after your attempt
Correct Answer
A. ((0,2))
Step 1
Concept
(A'=\(0,\infty\)) and (B'=\(-\infty,2\)). Their intersection is ((0,2)).
Step 2
Why this answer is correct
The correct answer is A. ((0,2)). (A'=\(0,\infty\)) and (B'=\(-\infty,2\)). Their intersection is ((0,2)).
Step 3
Exam Tip
(A'=\(0,\infty\)) और (B'=\(-\infty,2\)) हैं। उनका प्रतिच्छेद ((0,2)) है।
Login to save your score, XP, coins and progress. Login
यदि \(U={1,2,\ldots,8}\), \(A=\{1,2,5\}\), \(B=\{2,4,6\}\), तो \(A' \cup B'\) क्या है?
If \(U={1,2,\ldots,8}\), \(A=\{1,2,5\}\), and \(B=\{2,4,6\}\), what is \(A' \cup B'\)?
#sets
#de-morgan
#union-of-complements
#finite-set
A ({1,3,4,5,6,7,8})
B ({2})
C ({3,7,8})
D ({1,2,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({1,3,4,5,6,7,8})
Step 1
Concept
By De Morgan, (A' \cup B'=\(A \cap B\)'). Since \(A \cap B={2}\), the complement is ({1,3,4,5,6,7,8}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,4,5,6,7,8}). By De Morgan, (A' \cup B'=\(A \cap B\)'). Since \(A \cap B={2}\), the complement is ({1,3,4,5,6,7,8}).
Step 3
Exam Tip
डी मॉर्गन से (A' \cup B'=\(A \cap B\)') है। \(A \cap B={2}\), इसलिए पूरक ({1,3,4,5,6,7,8}) है।
Login to save your score, XP, coins and progress. Login
यदि (n(A')=35), (n(B')=42), (n(U)=80) और (n\(A\cap B\)=25) है, तो (n\(A'\cap B'\)) कितना है?
If (n(A')=35), (n(B')=42), (n(U)=80), and (n\(A\cap B\)=25), what is (n\(A'\cap B'\))?
#sets
#venn-diagrams
#complements
#two-sets
A (22)
B (18)
C (25)
D (12)
Explanation opens after your attempt
Step 1
Concept
(n(A)=45) and (n(B)=38), so (n\(A\cup B\)=45+38-25=58). The outside part is (80-58=22).
Step 2
Why this answer is correct
The correct answer is A. (22). (n(A)=45) and (n(B)=38), so (n\(A\cup B\)=45+38-25=58). The outside part is (80-58=22).
Step 3
Exam Tip
(n(A)=45) और (n(B)=38), इसलिए (n\(A\cup B\)=45+38-25=58)। बाहर का भाग (80-58=22) है।
Login to save your score, XP, coins and progress. Login
