Logic Worksheet With Answers Page 9
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22(~p q) r
b. “I do not fail the course if and only if I study hard, and I pass the final”
Part 3: Truth Tables for Negation, Conjunction, and Disjunction
Negation (not): Opposite truth value from the statement.
p
~p
T
F
F
T
Conjunction (and): Only true when both statements are true.
p
q
pq
T
T
T
T
F
F
F
T
F
F
F
F
Disjunction (or): Only false when both statements are false.
p
q
pq
T
T
T
T
F
T
F
T
T
F
F
F
Ex: Ex: Let p and q represent the following statements:
p: 100 > 0
q: -4 < 15
Since both statements are true, then p
q is true and p
q is true. The statement ~p
q will be false
because ~p is false.
Ex: Construct a truth table for ~(p q)
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