How many injective functions have domain [3], codomain [101], and are not surjective?

let A = { 1, 2, 3, 4, 5} and B = { a, b, c, d, e, f}. in each case, give an example of a function f : A-->B with indicated properties, or explain why no such function exist. a) f : A--->B, f is one-to-one b) g: B--> A, g is one-to-one c) f : A---> B, f is onto d) g: B-->A, g is onto

It was noted that the binary propositional operators, A and V, can be regarded as functions, f: B x B B. Explain why there exist 16 such functions in all.

Z is the set of integers, R is the set of real numbers. 5) Functions f: R -> R, g: R -> R are both one to one on the setof real numbers R. Is the function f + g also one to one?Prove your answer.