Construct truth table method whether or contra dictary it contingency, tautology Po(~po~2)

This is true only when both $\sim P$ and $\sim Q$ are true.

$P$	$Q$	$\sim P$	$\sim Q$	$\sim P \land \sim Q$
T	T	F	F	F
T	F	F	T	F
F	T	T	F	F
F	F	T	T	T

This is true if $P$ is true, or if $(\sim P \land \sim Q)$ is true, or both.

$P$	$Q$	$\sim P$	$\sim Q$	$\sim P \land \sim Q$	$P \lor (\sim P \land \sim Q)$
T	T	F	F	F	T $\lor$ F = T
T	F	F	T	F	T $\lor$ F = T
F	T	T	F	F	F $\lor$ F = F
F	F	T	T	T	F $\lor$ T = T

The final column for $P \lor (\sim P \land \sim Q)$ contains both 'T' (True) and 'F' (False) values.

• If all values were 'T', it would be a tautology.
• If all values were 'F', it would be a contradiction.
• Since it contains a mix of 'T' and 'F', it is a contingency.

The statement $P \lor (\sim P \land \sim Q)$ is a contingency.