State, whether the is given the statement, is True or False.
$\sim [(p \lor \sim q) \to (p \land \sim q)] \equiv (p \lor \sim q) \land (\sim \lor q)$

True

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False

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Solution

The correct option is A True
$p$ $q$ $\sim q$ $(p \lor \sim q)$ $(p \land \sim q)$ $(p \lor \sim q) \to (p \land \sim q)$
$\sim [(p \lor \sim q) \to (p \land \sim q)]$
$T$ $T$ $F$ $T$ $F$ $F$ $T$
$T$ $F$ $T$ $T$ $T$ $T$ $F$
$F$ $T$ $F$ $F$ $F$ $T$ $F$
$F$ $F$ $T$ $T$ $F$ $F$ $T$
$p$ $q$ $\sim q$ $(p \lor \sim q)$ $\sim p$
$(\sim p \lor q)$ $(p \lor \sim q) \land (\sim p \lor q)$
$T$ $T$ $F$ $T$ $F$ $T$ $T$
$T$ $F$ $T$ $T$ $F$ $F$ $F$
$F$ $T$ $F$ $F$ $T$ $T$ $F$
$F$ $F$ $T$ $T$ $T$ $T$ $T$

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Question 52

State whether the given statement is True or False.

If $\frac{p}{q}$ is a rational number and m is a non-zero common divisor of p and q, then $\frac{p}{q} = \frac{p \div m}{q \div m} .$

\cap

\cup

\cap

\cup

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