Logic Worksheet With Answers Page 10
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22First list the simple statements on top and show all the possible truth values.
Second, make a column for p q and fill in the truth values.
Third, construct one more column for ~(p q). The final column tells us that the statement is
false only when both p and q are true.
p q
~(p q)
p q
T T
T
F
T F
F
T
F T
F
T
F F
F
T
A compound statement that is always true is called a tautology. From the table, that means that
on its column need to be only Ts, no Fs.
Ex:
p: Brazosport College is a college. (true)
q: UHCL is an university. (true)
~(p q):
“It is not true that BC is a college and UHCL is an university”.
The compound statement ~(p q) is not a tautology because on the last column it contains at
least one F.
Ex: A truth table for (~p q) ~q:
~p q
(~p q) ~q
p
q
~p
~q
T
T
F
T
F
F
T
F
F
F
T
F
F
T
T
T
F
F
F
F
T
T
T
T
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