(1) |P(A)| = 4 <-- Cardinality of the power set is 4, which means we have 2^n = 4.** |A| = 2**

(2) |B| = |A|+ 1 and |A×B| = 30

|B| = 6 if **|A| = 5** and |A x B| = 30

(3) |B| = |A|+ 2 and |P(B)|−|P(A)| = 24

Since |B| = |A|+ 2, we have: 2^(a + 2) - 2^a = 24

2^a(2^2 - 1) = 24

2^a(3) = 24

2^a = 8

**|A |= 3**

To check, we have |B| = |A| + 2 --> 3 + 2 = 5

So |P(B)| = 2^5 = 32

|P(A)| = 2^3 = 8

And 32 - 8 = 24