Show that ~ (p∧q) and ~p∧~q are logically equivalent

Prove that the expressions (P double arrow Q)n-ary logical and (Q double arrow P) and P left right double arrow Q are logically equivalent (have the same truth table). Why does this make sense?

Define the logical connective "nand" (not and) by p wedge^OverBar q Longleftrightarrow not (p wedge q). Find a representation of each of the following statements that does not use negation (not) and in which the only logical connective used is nand. not p p wedge q p vee q Explain why every statement is logically equivalent to a statement that does not use negation (wedge) and in which the only logical connective used is nand.

Let , show that the following are equivalent. In