Use the set identities given in the table to prove the following new identities. Label each step in your proof with the set identity used to establish that step.

(a) (A C) (A C) = C

Express the following sets using the roster method. Express the elements as strings, not n-tuples.

(a){0x: x {0, 1}2}

(b){0, 1}0 {0, 1}1 {0, 1}2

(c){0x: x B}, where B = {0, 1}0 {0, 1}1 {0, 1}2.

(d){xy: where x {0} {0}2 and y {1} {1}2}

(e){xy: x {aa, ab} and y {a} {a}2}