The logical statement (p rightarrow q) wedge | vedclass

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(A) Given the logical statement: $(p$ $\rightarrow q) \wedge (p$ $\rightarrow \sim p)$ Using the implication law $a \rightarrow b \equiv \sim a \vee b

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$\sim p$

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(A) Given the logical statement: $(p$ $\rightarrow q) \wedge (p$ $\rightarrow \sim p)$ Using the implication law $a \rightarrow b \equiv \sim a \vee b$: $(p \rightarrow q) \equiv \sim p \vee q$ $(p \rightarrow \sim p) \equiv \sim p \vee \sim p \equiv \sim p$ Now,the expression becomes: $(\sim p \vee q) \wedge (\sim p)$ Using the absorption law: $A \wedge (A \vee B) \equiv A$ Here,let $A = \sim p$ and $B = q$. So,$(\sim p) \wedge (\sim p \vee q) \equiv \sim p$ Therefore,the statement is equivalent to $\sim p$.

The logical statement $(p$ $\rightarrow q) \wedge (p$ $\rightarrow \sim p)$ is equivalent to

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