Let `S = {1, 2, 3, 4).` The number of functions `f: S->S.`Such that `f(i) le 2i` for all `i in S` is

Let A={1,2,3,4,5} and f:A rarr A be an into function such that f(i) nei, forall i in A , then number of such functions f are

Let S= {1,2,3,4 5,6, 7} . Then the number of possible functions f: S rarr S such that f(m.n)= f(m).f(n) for every m, n in S and m.n in S is equal to ____

Let S = {1, 2, 3} . Determine whether the functions f : S->S defined as below have inverses. Find f^(-1) , if it exists.(a) f = {(1, 1), (2, 2), (3, 3)} (b) f = {(1, 2), (2, 1), (3, 1)} (c) f =

Let S = {1, 2, 3} . Determine whether the functions f : S->S defined as below have inverses. Find f^(-1) , if it exists.(a) f = {(1, 1), (2, 2), (3, 3)} (b) f = {(1, 2), (2, 1), (3, 1)}

Let S = {1, 2, 3} Determine whether the functions f : S rarr S defined as below have inverses. Find f ^–1 , , if it exists: f = {(1,3), (3,2), (2,1)}

Let S = {1, 2, 3} Determine whether the functions f : S rarr S defined as below have inverses. Find f ^–1 , , if it exists: f = {(1,2), (2,1), (3,1)}

Let S" "=" "{1," "2," "3} . Determine whether the functions f" ":" "S->S defined as below have inverses. Find f^(-1) , if it exists. (a) f" "=" "{(1," "1)," "(2," "2)," "(3," "3)} (b) f" "=" "{(1," "2)," "(2," "1)," "(3," "1)} (c) f" "=" "