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(C) The given statement pattern is $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q) = F$.Since the disjunction is $F$, all component

Vedclass · Accepted Answer

$T, T$

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(C) The given statement pattern is $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q) = F$.Since the disjunction is $F$, all components must be $F$: $(\sim p \land q) = F$, $(\sim p \land \sim q) = F$, and $(p \land \sim q) = F$.From $(\sim p \land q) = F$ and $(\sim p \land \sim q) = F$, we can factor out $\sim p$: $\sim p \land (q \lor \sim q) = F$. Since $(q \lor \sim q)$ is a tautology $(T)$, we have $\sim p \land T = F$, which implies $\sim p = F$, so $p = T$.Now substitute $p = T$ into $(p \land \sim q) = F$: $T \land \sim q = F$, which implies $\sim q = F$, so $q = T$.Now evaluate $(p \lor \sim q) = (T \lor \sim T) = (T \lor F) = T$.Now evaluate $(p 	o q) = (T 	o T) = T$.Thus, the truth values are $T, T$.

If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

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If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

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If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

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For the given statement,identify the necessary and sufficient conditions.
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