समुच्चय \(A=\{1,2,3,4\}\) पर संबंध \(R={(a,b)\in A\times A:a+b\) सम है(}) दिया है। (R) के equivalence classes कौन से हैं?
On the set \(A=\{1,2,3,4\}\), relation \(R={(a,b)\in A\times A:a+b\) is even(}) is given. What are the equivalence classes of (R)?
Explanation opens after your attempt
Correct Answer
A. ({1,3}) और ({2,4})({1,3}) and ({2,4})
Concept
(a+b) is even exactly when (a) and (b) have the same parity. Hence the equivalence classes are the odd class ({1,3}) and the even class ({2,4}).
Why this answer is correct
The correct answer is A. ({1,3}) और ({2,4}) / ({1,3}) and ({2,4}). (a+b) is even exactly when (a) and (b) have the same parity. Hence the equivalence classes are the odd class ({1,3}) and the even class ({2,4}).
Exam Tip
(a+b) सम तभी होता है जब (a) और (b) दोनों समान parity के हों। इसलिए equivalence classes विषम ({1,3}) और सम ({2,4}) हैं।
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