Which of the following collections of subsets form a partition of the set of integers? Provide some justification foryour answer.

1. The set of positive integers and the set of negative integers. (1 point)

YES: or NO:

Justification:

2. The set of integers not evenly divisible by 2, the set of even integers, and the set of integers leaving a remainder

of 3 when divided by 6. (1 point)

YES: or NO:

Justification:

Prove each statement that is true and give a counter-example for each statement that is false. (2 points, 1 point each)

1. (A B) = (A) (B)

2. (A) (B) (A B)