8– DeMorgan’s Law
Note:
The tilde (~) is used to denote a logical inversion, or NOT, operation.
The
symbol v is used to represent the OR operator, while the ^ symbol
represents the AND operator.
For
problems 1-4, use truth tables to determine if each pair of propositions are
equivalent
1. Ø (p ^ q)
Øp v Øq
e.g. is Ø (p ^ q) equivalent to Øp v Øq for every combination of
truth values of p and q?
2. Ø (p ^ q)
Øp v q
3. Ø (p v q)
Øp ^ Øq
4. Øp ^ q
Ø (p v Øq)
For
problems 5-8 attempt to simplify the expression by applying DeMorgan’s law.
5. Ø (Øp v q)
6. Ø (Øp v Øq)
7. Øp ^ (Øq v Ør)
8. Ø (Øp v q) ^ Ør