For two propositions p and q, let the logical operator NAND (an abbreviation for NOT AND) be dened as p NAND q = (p q). We can use the NAND operator...

For two propositions p and q, let the logical operator NAND (an abbreviation for NOT AND)

be defined as p NAND q = ∼(p ∧ q).

We can use the NAND operator to express the negation operator as follows: ∼p ≡ p NAND p.

(a) Show how to use the NAND operator to express the disjunction operation ∧ (AND) by

showing how to write p ∧ q using propositions p, q, and NAND operators.

(b) Do the same for the conjunction operator ∨ (OR): Show how to express p ∨ q using

propositions p, q and NAND operators.