1 Use two different methods to describe the set of positive even integers that are less than 20. 2. Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C , please use Venn diagram to show that A

1 Use two different methods to describe the set of positive even integers that are less than 20.

2. Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C , please use Venn diagram to show that A ⊆ C.

3. Please prove the theorem: for every set S, we have ∅ ⊆ S and S ⊆ S.

4. Use mathematical induction to show that 1 + 2 + 2^2+ 2^3 + ⋯ + 2^n = 2^n+1 − 1 For all nonnegative integers n