- #1

- 1,270

- 0

**1) Let N={natural numbers}. What is the cardnality of the set of all functions from N to {1,2,7}, |N| or c or 2**

^{c}?[attempt: If it's the other way around, i.e. {all functions from {1,2,7} to N}, then I know that it has cardnality |NxNxN|=|N|]

**2) Assume that |A1|=|B1| and |A2|=|B2|.**

2a) Prove that |A1 x A2| = |B1 x B2|.

2b) If A1 is disjoint from A2 and B1 is disjoint from B2, then |A1 U A2|=|B1 U B2|.

2a) Prove that |A1 x A2| = |B1 x B2|.

2b) If A1 is disjoint from A2 and B1 is disjoint from B2, then |A1 U A2|=|B1 U B2|.

[attempt: |A1|=|B1| means there exsits f: A1->B1 that is one-to-one and onto]

Can someone give me some general hints on these questions, please? Any help would be greatly appreciated!