Most Important Selected Qs for JEE AdvancedMathematicsSets and Relations

A relation on the set of real number R is defined as x y: x y>0 . Then, which of the following is/are true?

Options

Ais reflexive and symmetric
Bis symmetric but not reflexive
Cis symmetric and transitive
Dis an equivalence relation

Correct answer

C. is symmetric and transitive

Step-by-step solution

We have, x p y: x y>0 (i) Reflexive Suppose x x R x² > 0 which is not true when x=0 . Hence, relation is not reflexive. (ii) Symmetric x p y R x y>0 y x>0 y x R If (x, y) R, then, relation is symmetric. (iii) Transitive xp y R x y>0 and y z Ry z>0 array lc & x y² z>0 & x z>0 & (x, z) R If (x, y) R, then (y, z) R & (x, z) R array Hence, relation is transitive.

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