For each of the following propositions, construct a truth table showing a column for each

operator. If there is a biconditional, represent it with three columns; two columns for

each of the two implications and the third column for the 'AND' of the implications.

Indicate whether the proposition is a tautology, a contradiction, or a contingency.

$(PvvQ)(not(PQ))(notP)$

$(P^{{?}^{?}}{Q}^{{?}^{?}}R{)}^{{?}^{?}}(notPvvnotQvvnotR)$

$(P^{{?}^{?}}{Q}^{{?}^{?}}R)V(notPvvnotQvvnotR)$

$(P^{{?}^{?}}R{)}^{{?}^{?}}$not$(PvvnotQ)$

$(P=>Q)VnotQ$

$(P^{{?}^{?}}$notQ$)=>$not$(P=>Q)$

$(P=>Q)>(notQ=>$notP$)$

$(not{P}^{{?}^{?}}$notQ$)>$not$(P^{{?}^{?}}Q)$