Let r be a relation from R (set of real numbers) to R defined by r= (a,b) a,b R and a-b+ 3 is an irrational number . The relation r is

JEE Main Mathematics question

Let be a relation from (set of real numbers) to defined by . The relation is

(A)An equivalence relation
(B)Reflexive onlyCorrect
(C)Symmetric only
(D)Transitive only

Answer: (B)

Solution

Check the three properties one by one. Reflexive: put . Then , which is irrational, so for every real . Hence IS reflexive. Symmetric: take , . Then (irrational), so . But for the reversed pair, , which

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Question ID VK-007323