Problem 1. Let A = {5k : k N}. Prove |A| = |N| by constructing an explicit bijectionbetween A and N and proving that it is indeed a bijection.

Problem 2. Assume A and B are two non-empty sets such that A B = . Assume |A| = nfor some n N and |B| = |N|. Prove that |A B| = |N|.For this problem specify and explicit bijection between A B and N, but you do notneed to prove it is a bijection in a rigorous way.

Problem 3. Assume A and B are two non-empty sets such that A B = . Assume |A| = Nand |B| = |N|. Prove that |A B| = |N|.For this problem specify and explicit bijection between A B and N, but you do notneed to prove it is a bijection in a rigorous way. Looking at the proof we did in class for|N| = |Z| might be useful.

N = all natural numbers (0,1,2,3,4,..etc)

Z = all integers(positive and negative)