Quiz 4

Show all work in a neat and organized fashion. Clearly indicate your answers.

10 points possible.

1. (3 pts.) For the following relation, find R^-1.

R={(x,y):x,y Î N, x | y}

2. (3 pts.) Consider the relation Í on 2 ^Z (i.e., the ``is-a-subset-of'' relation defined on all sets of integers). Prove or disprove: Í is symmetric.

3. (4 pts.) Let R, S, and T denote sets. Prove that

(R - S)×T=(R×T) - (S×T).