Consider the following relations: R = {( x , y ) ∣ x , y are real numbers and x = wy for some rational number w } ; S = { ( n m , q p ) ∣ m , n , p and q are integers such that n , q  = 0 and q m

Question

Consider the following relations: R = {( x , y ) ∣ x , y are real numbers and x = wy for some rational number w } ; S = { ( n m ​ , q p ​ ) ∣ m , n , p and q are integers such that n , q  = 0 and q m = p n } . Then

TestHub · Accepted Answer

xRy need not implies y R x S : n m ​ s q p ​ ⇔ qm = pn n m ​ s n m ​ reflexive n m ​ s q p ​ n m ​ s q p ​ , q p ​ s s r ​ ​ ⇒ q p ​ s n m ​ symmetric ⇒ q m = p n , p s = r q ⇒ m s = r n transitive. ​ S is an equivalence relation.

Mathematics - Sets and Relations Question with Solution | TestHub

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JEE Main 2028 (Class 11)