(a) Let X = {1,2,3,4} and Y = {a,b,c}. Define H :X→Y as follows: Н(1) — с, Н(2) %3 а, Н(3) — с, Н(4) — b. Is H onto? (b) Let X = {1,2,3} and Y = {a,b,c,d}. Define H : X → Y as follows: Н(1) — с, Н(2)...

Extracted text: (a) Let X = {1,2,3,4} and Y = {a,b,c}. Define H :X→Y as follows: Н(1) — с, Н(2) %3 а, Н(3) — с, Н(4) — b. Is H onto? (b) Let X = {1,2,3} and Y = {a,b,c,d}. Define H : X → Y as follows: Н(1) — с, Н(2) — а, and H(3) — d. Is H one-to-one? (c) Define a function G : N → Z+ as follows: For all x E Z, F(x) = |x| +1. • Is G one-to-one? Is G onto? Prove or give a counterexample.