Let F(R, R) be the set of all functions from R to R. For any f, g € F(R, R), we define fog € F(R, R) by setting (fog)(a) = f(g(a)) for all a € R. (a) Prove or disprove that o is associative. (b) Prove or disprove that is commutative.

A function g : Z → Z is defined as g(n) = |n| + 1. Show that this function is not injective and not surjective.

Choose the correct option. The number of onto function from the set {1,2,….,11} to the set {1,2,….,10} is- (a)5×⌊11        (b)⌊10           (c)⌊11/2         (d)10×⌊11

(a) What is the number of onto functions f : {1,2, 3, 4, 5} → {1, 2, 3}? (b) What is the number of one to one functions f : {1,2, 3} → {1,2, 3, 4, 5}?

DISCRETE MATHEMATICS:

Determine whether each of these functions f:Z->Z is one-to-one, on-to, one-to-one correspondence, respectively. a) f(n) = n-1 b) fln)= n² +1 c) f(n)= n² d) fir) = [n/2]

1. Let A = {1,2,3}, B = B = {4,5,6}, The functions f : A → C and g: B → C are defined by f(1) = 7, f(2)= 9, f(3) = 7, Does there exist a function h: A → B such that go h = f? Does there exist a function k : B → A such that fo k = g? Justify your answers. {4,5,6}, C = {7, 8, 9, 10}. g(4) = 10, g(5) = 7, g(6) = 9.

Let f: P(N) → P(N) be the f(X) =X∪{8,9} defined function. 1)What is the value when f({6,8})? 2) what is the relationship of f 3)The image of f is? Choose one A) N B) P(N) C) P({8,9}) D) {8,9} E) {X:X∈ P(N) and {8,9}⊆ X} F) All is wrong

please just answer (d)