# a) What is the minimum number of pairs to form a non-zero reflexive relation on a set of n elements?

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a) What is the minimum number of pairs to form a non-zero reflexive relation on a set of n elements?

b) On the set R of real numbers, S is a relation defined as S = {(x,y)/X∈R, y ∈ R, x + y = xy}. Find a ∈ R such that ‘a’

is never the first element of an ordered pair in S. Also find b ∈ R such that ‘b’ is never the second element of an ordered pair in S.

c) Consider the function f(x)=$\frac{3x + 4}{x-2}$,x≠2 Find a function on a suitable domain such that goƒ(x) = x = ƒog(x).

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a) n

b) a + y  = ay ⇒ ay - y = a ⇒ y (a - 1) = a

⇒ $y = \frac{a}{a-1}$ ⇒ a ≠ 1

similarly; b ≠ 1

c) go f(x) = x = f og (x) ⇒ g(x) = f-1 (x)

f (x) = $\frac{3x + 4}{x - 2}$ = y ⇒ 3x + 4 = y(x-2)

⇒ 3x + 4 = yx - 2y ⇒ yx - 3x = 2y + 4

⇒ x = $\frac{2y + 4}{y - 3}$

⇒ g(x) = $\frac{2x + 4}{x-3}$