The statement p rightarrow (q rightarrow p) i | vedclass

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(B) The given statement is $p$ $\rightarrow (q$ $\rightarrow p)$.Using the logical equivalence $A \rightarrow B \equiv \sim A \vee B$,we have:$p$ $\ri

Vedclass · Accepted Answer

$p \rightarrow (q \vee p)$

Vedclass · Answer

(B) The given statement is $p$ $\rightarrow (q$ $\rightarrow p)$.Using the logical equivalence $A \rightarrow B \equiv \sim A \vee B$,we have:$p$ $\rightarrow (q$ $\rightarrow p) \equiv \sim p \vee (\sim q \vee p)$.By the associative and commutative laws,this is equivalent to $(\sim p \vee p) \vee \sim q$,which simplifies to $T \vee \sim q = T$ (a tautology).Now,let us check option $B$: $p \rightarrow (q \vee p) \equiv \sim p \vee (q \vee p) \equiv (\sim p \vee p) \vee q \equiv T \vee q = T$.Since both expressions are tautologies,the statement $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to $p \rightarrow (q \vee p)$.

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

Similar Questions

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