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  4. In the truth table for the statement (∼ p ∨ q ) arrow[ p ∧( q ∨ ∼ q )], the last column has the truth value in the following order is

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Q. In the truth table for the statement $(\sim p \vee q ) \rightarrow[ p \wedge( q \vee \sim q )]$, the last column has the truth value in the following order is

Mathematical Reasoning

Solution:

$\sim[\sim p \vee q ] \vee[ p \wedge( q \vee \sim q )]=[\sim(\sim p )] \wedge(\sim q ) \vee[ p \wedge t ]$
$=[ p \wedge(\sim q )] \vee t = t$