Logic Worksheet With Answers Page 16
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Ex: Let’s prove the equivalence: ~(p q)
p
~q.
p
q
p q
~(p q)
~q
p
~q.
T
T
T
F
F
F
T
F
F
T
T
T
F
T
T
F
F
F
F
F
T
F
T
F
The negation of a conditional statement can be expressed in the following way:
~(p q)
p
~q.
Ex: The negation of the statement “If too much homework is given, a class should not be taken”
can be formed using:
p: Too much homework is given,
q: A class should be taken.
The symbolic form is p ~q. The negation of p ~q is p ~(~ q) which simplifies to p q.
Translating this one into English we have: “Too much homework is given and a class should be
taken.”
De Morgan’s Laws:
1. ~(p
q)
~p
~q;
2. ~(p
q)
~p
~q;
Ex: The first law is shown in the truth table below.
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