Which of the following statements is a contin | vedclass

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(C) Key Idea: $A$ statement that is neither a tautology nor a contradiction is a contingency.Option $A$: $(p \vee q) \vee \sim q \equiv p \vee (q \vee

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$(p \vee q) \wedge \sim q$

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(C) Key Idea: $A$ statement that is neither a tautology nor a contradiction is a contingency.Option $A$: $(p \vee q) \vee \sim q \equiv p \vee (q \vee \sim q) \equiv p \vee T \equiv T$. This is a tautology.Option $B$: $(p \vee q) \vee \sim p \equiv (p \vee \sim p) \vee q \equiv T \vee q \equiv T$. This is a tautology.Option $C$: $(p \vee q) \wedge \sim q \equiv (p \wedge \sim q) \vee (q \wedge \sim q) \equiv (p \wedge \sim q) \vee F \equiv p \wedge \sim q$. If $p=T, q=T$,then $p \wedge \sim q = F$. If $p=T, q=F$,then $p \wedge \sim q = T$. Since the truth value depends on $p$ and $q$,it is a contingency.Option $D$: $p \rightarrow (p \vee q) \equiv \sim p \vee (p \vee q) \equiv (\sim p \vee p) \vee q \equiv T \vee q \equiv T$. This is a tautology.Therefore,the correct statement is $(p \vee q) \wedge \sim q$.

Which of the following statements is a contingency?

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