The statement pattern p rightarrow (q rightar | vedclass

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Question

(B) To determine the equivalent statement,we evaluate the truth table for the given pattern $p$ $\rightarrow (q$ $\rightarrow p)$ and compare it with

Vedclass · Accepted Answer

$p \rightarrow (p \vee q)$

Vedclass · Answer

(B) To determine the equivalent statement,we evaluate the truth table for the given pattern $p$ $\rightarrow (q$ $\rightarrow p)$ and compare it with the options.| $p$ | $q$ | $q \rightarrow p$ | $p$ $\rightarrow (q$ $\rightarrow p)$ ||---|---|---|---|| $T$ | $T$ | $T$ | $T$ || $T$ | $F$ | $T$ | $T$ || $F$ | $T$ | $F$ | $T$ || $F$ | $F$ | $T$ | $T$ |The statement $p$ $\rightarrow (q$ $\rightarrow p)$ is a tautology (always true).Now,check option $B$: $p \rightarrow (p \vee q)$.| $p$ | $q$ | $p \vee q$ | $p \rightarrow (p \vee q)$ ||---|---|---|---|| $T$ | $T$ | $T$ | $T$ || $T$ | $F$ | $T$ | $T$ || $F$ | $T$ | $T$ | $T$ || $F$ | $F$ | $F$ | $T$ |Since both $p$ $\rightarrow (q$ $\rightarrow p)$ and $p \rightarrow (p \vee q)$ result in a tautology,they are logically equivalent.Thus,the correct option is $B$.

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

Similar Questions

Let $a : \sim (p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false,then the truth values of $a$ and $b$ are respectively:

Write the negation of the following statement:
$\sqrt{2}$ is not a complex number.

Negation of $p \wedge (\sim q \vee \sim r)$ is -

Which of the following statements is a tautology?

Write the negation of the following statement:
$p:$ For every positive real number $x,$ the number $x-1$ is also positive.

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