For this question, we introduce two new connectives, NAND and XOR. For a truth as-signment v, we define the truth values of two new connectives as follows: v(p NAND q) is true if and only if v(p) and v(q) are not both true at the same time, and v(p XOR q) is true if and only v(p) ? v(q). See also the truth tables for NAND and XOR below.

(a) Prove that {NAND} is an adequate set of connectives (that is, NAND is adequate on its own!).

(b) Prove that {XOR} is not an adequate set of connectives.

q TT TF FT FF (p NAND q) (p XOR q) F F T T T T T F