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Question

Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
$$ \sim (\sim q \wedge p) \wedge q $$


Solution

$$p\ \ \ $$$$q\ \ \ $$$$\sim q\ \ \ $$$$q\,\wedge 
\sim p\ \ \ $$
$$\sim (\sim q
\wedge p)\ \ \ $$
$$ \sim (\sim q
\wedge p) \wedge
q $$
TT  F      F       T           F
TF  T      T       F           F
FT  F      F       T           T
FF  T      F       T           F

The entries in the last column of the above truth table are neither all T nor a F.
$$ \therefore \,\sim (\sim q \wedge p) \wedge q $$ is a contingency.

Maths

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