# (i) Let R be the relation on the set N of natural numbers given by R = {(a,b): a – b > 2, b>3} Choose the correct answer

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(i) Let R be the relation on the set N of natural numbers given by

R = {(a,b): a – b > 2, b>3}

(a) (4, 1) ∈ R

(b) (5, 8) ∈ R

(c) (8, 7) ∈ R

(d) (10, 6) ∈ R

(ii) If ƒ(x) = 8x3 and g(x) = x1/3, findg(ƒ(x)) and ƒ(g(x))

(iii) Let * be a binary operation on the set Q of rational numbers defined by a*b = $\frac{a}{b}$. Check whether * is commutative and associative?

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(i) (d) (10,6) ∈ R

(ii) Given ; f(x) = 8x3 and g(x) = x1/3

g(f(x)) = g(8x3) = (8x3)1/3 = 2x

f(g(x)) = f(x1/3) = 8(x1/3)3 = 8x

(iii) a*b = $\frac{ab}{3} = \frac{ba}{3}$ = b*a

Hence commutative

a*(b*c) = a*$\frac{bc}{3}$ = $\frac{abc}{9}$

(a*b)*c = $\frac{ab}{3}$ * c = $\frac{abc}{9}$

a*(b*c) = (a*b)*c

Hence associative