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Let A={2, {2}, (2)2}, B= {2, {2{, {{2}} and C={2}. Evaluate the truth and falsity of the following statements.
Show that the functions, defined by f:R->(1,infinity) ->R f(x)=3^2x+1, g(x)=log(x-1) are inverse of one another.
Let X = {a, b, c} defined by f : X
If a function is defined as f(x,n) mod n. Determine the

i. Domain of f

ii. Range of f

iii. G(g(g(g(7)))) if g (n) = f(209, n).
Determine whether the following relations are injective and/or subjective function. Find universe of the functions if they exist.

i. A= v,w,x,y,z, B=1,2,3,4,5

R= (v,z),(w,1), (x,3),(y,5)

ii. A = 1,2,3,4,5 B=1,2,3,4,5

R = (1,2),(2,3),(3,4),(4,5),(5,1)
Check the extension of d given by d(x,y) = d(x,a) + 1 + d(b,y) where x belongs to X and y belongs to Y/ X
Define a bijective function. Explain with reasons whether the following functions are bijective or not. Find also the inverse f(x) = (2x+3) mod7, A=N7
Show that the functions f: R -->1 , infinity -->R , defined by : x=3^2x +1 , x= log x-1 are inverse of one another.
Let L = {3, 4, 12, 24, 48, 82} and the relation < be defined on L such that x < y if x divides y. Draw the Hasse diagram.
Let X = {a, b, c} defined by f : X
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