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Question

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


A
p(pq)
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B
p(pq)
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C
p(pq)
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D
p(pq)
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Solution

The correct option is B $$p\rightarrow(p\vee q)$$
$$p\rightarrow(q\rightarrow p)=\sim p\vee (q\rightarrow p)=\sim p\vee \left( \sim q\vee p \right)=\sim p\vee p\vee q=T\vee q=T $$
Since $$p\vee \sim p$$ is always true
$$p\rightarrow(p\vee q)=\sim p\vee p\vee q=T\vee q=T $$

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