Define a new sentential connective ∇, called nor, by the following truth table. (a) Use a truth table to show that p ∇ p is logically equivalent to ~ p. (b) Complete a truth table for ( p ∇ p) ∇ ( q ∇...

Define a new sentential connective ∇, called nor, by the following truth table.

(a) Use a truth table to show that p ∇ p is logically equivalent to ~ p.

(b) Complete a truth table for ( p ∇ p) ∇ ( q ∇ q).

(c) Which of our basic connectives ( p ∧ q, p ∨ q, p ⇒ q, p ⇔ q) is logically equivalent to ( p ∇ p) ∇ ( q ∇ q) ?