1. Argue that, for any sets A and B, |A ∪ B| = |A − B| + |B − A| + |A ∩ B|. (Use the Sum Rule.) 2. How many 100-bit strings have at most 2 ones? 3. Determine how many k-bit strings have exactly three...

1. Argue that, for any sets A and B, |A ∪ B| = |A − B| + |B − A| + |A ∩ B|. (Use the Sum Rule.)

2. How many 100-bit strings have at most 2 ones?

3. Determine how many k-bit strings have exactly three 1s using the approach in Example 9.4—that is, by dividing the set of bitstrings based on the position of the third one