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(i) If R = {(x,y) : x, y ∈ Z, x – y ∈ Z}, then the relation R is

(a) Reflexive but not transitive

(b) Reflexive but not symmetric

(c) Symmetric but not transitive

(d) An equivalence relation.

(ii) Let * be a binary operation on the set Q of rational numbers by a*b = 2a + b. Find 2 * (3 * 4) and (2 * 3) * 4.

(iii) Let ƒ : R → R, g : R → R be two one-one funçtions. Check whether gof is one-one or not.

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Best answer

(i) (d) An equivalance relation.

(ii) 2* (3 * 4) = 2 * 10 = 14

(2 * 3)* 4 = 7 * 4 = 18

(iii) ƒ : R → R, g : R → R

Let x1, x2, ∈ R

goƒ(x1) = g(ƒ(x1)) = g(ƒ(x2)) = g(ƒ(x2))

⇒ x1 = x2

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