Problem 7. Consider the operator NAND such that p NAND q is true when (1) p is false, q is true, or (2) P is true, q is false, or (3) both p and q are false; and it is false when both p and q are true. 7(a) Construct a truth table for NAND. hib) Prove that p NAND q is logically equivalent to (p). 7(c) Prove that NAND is commutative (that is, p NAND I = NAND p)