A. \(A\subseteq B\) और \(B\subseteq A\)/\(A\subseteq B\) and \(B\subseteq A\)
Step 1
Concept
If each set is a subset of the other, every member matches. Equal cardinality alone is not enough.
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\) और \(B\subseteq A\) / \(A\subseteq B\) and \(B\subseteq A\). If each set is a subset of the other, every member matches. Equal cardinality alone is not enough.
Step 3
Exam Tip
दोनों दिशाओं में उपसमुच्चय संबंध होने पर हर सदस्य समान होता है। केवल सदस्यों की संख्या बराबर होना काफी नहीं है।
The inequality (|x-2|<2) gives integer values (1,2,3), so the sets are equal. In exams solve the inequality first and write roster form.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The inequality (|x-2|<2) gives integer values (1,2,3), so the sets are equal. In exams solve the inequality first and write roster form.
Step 3
Exam Tip
(|x-2|<2) से पूर्णांक मान (1,2,3) मिलते हैं इसलिए दोनों समुच्चय बराबर हैं। परीक्षा में असमता को पहले हल करके रोस्टर रूप लिखें।
For finite sets, if one is a subset of the other and both have equal cardinality, no extra element remains so (A=B). In exams the finiteness condition is important.
Step 2
Why this answer is correct
The correct answer is A. (A=B). For finite sets, if one is a subset of the other and both have equal cardinality, no extra element remains so (A=B). In exams the finiteness condition is important.
Step 3
Exam Tip
सीमित समुच्चयों में उपसमुच्चय और समान सदस्य संख्या होने पर कोई अतिरिक्त तत्व नहीं बचता इसलिए (A=B)। परीक्षा में सीमितता की शर्त महत्वपूर्ण है।
The positive multiples of (5) less than (20) are (5,10,15), so the sets are equal. In exams do not include the boundary in "less than".
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive multiples of (5) less than (20) are (5,10,15), so the sets are equal. In exams do not include the boundary in "less than".
Step 3
Exam Tip
(20) से कम (5) के धनात्मक गुणज (5,10,15) हैं इसलिए दोनों बराबर हैं। परीक्षा में "से कम" में सीमा को शामिल न करें।
The odd natural numbers less than (9) are (1,3,5,7), so both are equal. In exams include the boundary only when the condition allows it.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The odd natural numbers less than (9) are (1,3,5,7), so both are equal. In exams include the boundary only when the condition allows it.
Step 3
Exam Tip
(9) से कम विषम प्राकृतिक संख्याएं (1,3,5,7) हैं इसलिए दोनों बराबर हैं। परीक्षा में सीमा के बराबर संख्या तभी लें जब शर्त अनुमति दे।
B. दोनों में वही तत्व हैं/Both have the same elements
Step 1
Concept
Order does not matter in a set and sets are equal when they have the same elements. In exams changing order does not change a set.
Step 2
Why this answer is correct
The correct answer is B. दोनों में वही तत्व हैं / Both have the same elements. Order does not matter in a set and sets are equal when they have the same elements. In exams changing order does not change a set.
Step 3
Exam Tip
समुच्चय में क्रम महत्व नहीं रखता और समान तत्व होने पर समुच्चय बराबर होते हैं। परीक्षा में क्रम बदलने से समुच्चय नहीं बदलता।
Repetition is removed in a set so the only elements are (L,E,V). In exams take unique letters in a set made from a word.
Step 2
Why this answer is correct
The correct answer is A. ({L,E,V}). Repetition is removed in a set so the only elements are (L,E,V). In exams take unique letters in a set made from a word.
Step 3
Exam Tip
समुच्चय में दोहराव हट जाता है इसलिए केवल (L,E,V) तत्व हैं। परीक्षा में शब्द से बने समुच्चय में अद्वितीय अक्षर लें।
Repeated elements in a set are counted only once so the sets are equal. In exams compare distinct elements not frequency.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Repeated elements in a set are counted only once so the sets are equal. In exams compare distinct elements not frequency.
Step 3
Exam Tip
समुच्चय में दोहराए गए तत्व केवल एक बार गिने जाते हैं इसलिए दोनों बराबर हैं। परीक्षा में आवृत्ति से नहीं बल्कि अलग तत्वों से तुलना करें।
The condition \(-2\le x<2\) excludes (2), so the elements are (-2,-1,0,1). In exams watch open and closed bounds carefully.
Step 2
Why this answer is correct
The correct answer is A. ({-2,-1,0,1}). The condition \(-2\le x<2\) excludes (2), so the elements are (-2,-1,0,1). In exams watch open and closed bounds carefully.
Step 3
Exam Tip
शर्त \(-2\le x<2\) में (2) शामिल नहीं है इसलिए तत्व (-2,-1,0,1) हैं। परीक्षा में खुली और बंद सीमा ध्यान से देखें।
Whole numbers start from (0) so for (x<3) we get \(B=\{0,1,2\}\). In exams remember the difference between (W) and (N).
Step 2
Why this answer is correct
The correct answer is A. (A=B). Whole numbers start from (0) so for (x<3) we get \(B=\{0,1,2\}\). In exams remember the difference between (W) and (N).
Step 3
Exam Tip
पूर्ण संख्याएं (0) से शुरू होती हैं इसलिए (x<3) पर \(B=\{0,1,2\}\) है। परीक्षा में (W) और (N) का अंतर याद रखें।
The roots of the equation are (2) and (3) so both sets have the same elements. In exams solve the equation first and then compare the sets.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The roots of the equation are (2) and (3) so both sets have the same elements. In exams solve the equation first and then compare the sets.
Step 3
Exam Tip
समीकरण के मूल (2) और (3) हैं इसलिए दोनों समुच्चयों के तत्व समान हैं। परीक्षा में पहले समीकरण हल करें फिर तुलना करें।
The symbol ({}) is the empty set so both (A) and (B) contain the same single element. In exams identify \(\emptyset\) and \({\emptyset}\) separately.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The symbol ({}) is the empty set so both (A) and (B) contain the same single element. In exams identify \(\emptyset\) and \({\emptyset}\) separately.
Step 3
Exam Tip
({}) वही रिक्त समुच्चय है इसलिए (A) और (B) दोनों में एक ही तत्व है। परीक्षा में \(\emptyset\) और \({\emptyset}\) को अलग पहचानें।
The positive primes less than four are only (2) and (3) so the sets are equal. In exams convert descriptive form into roster form.
Step 2
Why this answer is correct
The correct answer is B. (A=B). The positive primes less than four are only (2) and (3) so the sets are equal. In exams convert descriptive form into roster form.
Step 3
Exam Tip
चार से कम धनात्मक अभाज्य संख्याएं केवल (2) और (3) हैं इसलिए दोनों समुच्चय बराबर हैं। परीक्षा में गुण बताने वाली भाषा को रोस्टर रूप में बदलें।
For finite sets, if one is a subset of the other and both have the same number of elements, they are equal. This is a useful rule for proving equality.
Step 2
Why this answer is correct
The correct answer is A. (A=B). For finite sets, if one is a subset of the other and both have the same number of elements, they are equal. This is a useful rule for proving equality.
Step 3
Exam Tip
सीमित समुच्चयों में यदि एक दूसरे का उपसमुच्चय हो और दोनों में समान संख्या में अवयव हों, तो वे बराबर होते हैं। यह बराबरी सिद्ध करने का उपयोगी नियम है।
