De Morgan's Laws state that

• The negation of a conjunction of two statements is logically equivalent to the disjunction of the negations of the statements.
• The negation of the disjunction of two statements is logically equivalent to the conjunction of the negations of the statements

De Morgan's law combines conjunction and disjunction along with negation. Symbolically stated

• Ø (p Ù q)Û (Ø p Ú Ø q)
• Ø (p Ú q)Û (Ø p Ù Ø q)

A tautology is a statement that has the final value of "true" for all possible combinations for the variables.

A contradiction is a statement that always takes on the value "false." Hence a statement P is a contradiction if and only if (iff) Ø P is a tautology, and P is a tautology iff Ø P is a contradiction.

Determine whether each statement is a tautology, a contradiction, or neither.

1. p Ú Ø p
2. q Ù Ø q
3. Ø p Ú q