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(A) Given that $p = T$,$q = F$,and $r = T$. First,evaluate the statement pattern $S = [\sim q \wedge (p \vee \sim q) \wedge \sim r] \vee p$. Substitut

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$T, T$

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(A) Given that $p = T$,$q = F$,and $r = T$. First,evaluate the statement pattern $S = [\sim q \wedge (p \vee \sim q) \wedge \sim r] \vee p$. Substituting the values: $S = [\sim F \wedge (T \vee \sim F) \wedge \sim T] \vee T$ $S = [T \wedge (T \vee T) \wedge F] \vee T$ $S = [T \wedge T \wedge F] \vee T$ $S = F \vee T = T$. Next,find the dual statement $S^*$. To find the dual,replace $\wedge$ with $\vee$,$\vee$ with $\wedge$,$T$ with $F$,and $F$ with $T$. The dual statement is $S^* = [\sim q \vee (p \wedge \sim q) \vee \sim r] \wedge p$. Substituting the values: $S^* = [\sim F \vee (T \wedge \sim F) \vee \sim T] \wedge T$ $S^* = [T \vee (T \wedge T) \vee F] \wedge T$ $S^* = [T \vee T \vee F] \wedge T$ $S^* = T \wedge T = T$. Thus,the truth values are $T$ and $T$.

If the statements $p, q$ and $r$ are true,false and true statements respectively,then the truth value of the statement pattern $[\sim q \wedge (p \vee \sim q) \wedge \sim r] \vee p$ and the truth value of its dual statement respectively are

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