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

Question

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 (A) TTFF (B) FTFT (C) TFFT (D) TTTT

Tardigrade Admin · Accepted Answer

∼[∼ p ∨ q ] ∨[ p ∧( q ∨ ∼ q )]=[∼(∼ p )] ∧(∼ q ) ∨[ p ∧ t ] =[ p ∧(∼ q )] ∨ t = t

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

TTFF

FTFT

TFFT

TTTT

$\sim [\sim p \lor q] \lor [p \land (q \lor \sim q)] = [\sim (\sim p)] \land (\sim q) \lor [p \land t]$
$= [p \land (\sim q)] \lor t = t$

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