Logic Worksheet With Answers Page 12
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22Part 4: Truth Tables for the Conditional and the Biconditional
p q
Conditional
p q
p
q
T
T
T
T
F
F
F
T
T
F
F
T
Remark: A conditional is false only when the antecedent is true and the consequent is false.
Ex: A truth table for ~q ~p:
p
q
~q
~p
~q ~p
T
T
F
F
T
T
F
T
F
F
F
T
F
T
T
F
F
T
T
T
Ex: A truth table for [( p q) ~ p] q:
p
q
~p
p
q
( p
q)
~ p
[( p
q)
~ p]
q
T
T
T
F
F
T
T
F
T
F
F
T
F
T
T
T
T
T
F
F
F
T
F
T
Based on the results from the last column, this compound statement is a tautology.
p q
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