For each of the following functions, determine whether the function is: Injective (one-to-one). Surjective (onto). ⚫ Bijective. Justify your answers. 1.5 f: ZxZZ such that f(x, y) = xy.

Prove:Church’s thesis: The class of computable functions is equal to the class of intuitive computable functions.

Here are the definitions for functions f and g. f R R defined by f(x) = x2 g: R R defined by g(x) = x3 Answer the following questions 1) is fa 1-1 function? is fa onto function? is f a bijection? Does f have an inverse? If yes, what is the inverse of f? 1) is ga 1-1 function? is g an onto function? is g a bijection? Does g have an inverse? If yes, what is the inverse of g?

Let A = {1, 2, 3, 4} and B = {a, b, c}. Give an example of a function f: A -> B that is neither injective nor surjective.

Please written by computer source

Determine if each function is injective, surjective or bijective. Give one counterexample for each that it is not. 1. function f from {a,b,c,d} to itself, where f(a) = d,  f(b) = b,  f(c) = a,  f(d) = c

7. Let P denote the set of all phones in the world such that p ∈ P is a phone. Thus, S(p)denotes that “p is a SamsungTM phone”, N(p) denote that “p is a NokiaTM phone”, and G(p)denote that “p is a GoogleTM phone”. Therefore, express each of the following statements usingquantifiers, logical operations, and the propositional functions: S(p),N(p),G(p).(a) There is a GoogleTM phone that is also a SamsungTM phone.(b) Every NokiaTM phone is a GoogleTM phone.(c) No NokiaTM phone is a GoogleTM phone.(d) Some NokiaTM phones are also SamsungTM phones.(e) Some NokiaTM phones are also GoogleTM phones and some are not. PS: Please do not answer them in a paper format.

let A={a,b,c,d,e} and let b the set of letters in the alphabet. Let the functions f,g,h from A to B be defined as follow

how many functions a) map {1,2,3.4.5.6} to {up,down,left,right} b) how many functions in part a are subjective? c) how many have f- inverse(up) =2

Let A = {1, 2,3} and B = {a, b, c, d}   What is the function from a to b?