Consider : Statement - I : p ∧ ~ q ∧ ~ p ∧ q is a fallacy. Statement - II : p → q ↔ ~ q → ~ p is a tautology.

Question

Consider : Statement - I : p ∧ ~ q ∧ ~ p ∧ q is a fallacy. Statement - II : p → q ↔ ~ q → ~ p is a tautology., Statement - I is true; statement - II is false., Statement - I is false; Statement - II is true., Statement - I true; Statement - II is true; Statement - II is a correct explanation for Statement - I ., Statement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I .

MARKS App · Accepted Answer

The truth table for Statement I is p q ~ p ~ q p ∧ ~ q ~ p ∧ q p ∧ ~ q ∧ ~ p ∧ q T T F F T F T F F F T T F T F T F T F F F F T F F F F F Hence, it is a fallacy. The truth table for statement II is p q ~ p ~ q p → q ~ q → ~ p p → q ↔ ~ q → ~ p T T F F T F T F F F T T F T F T T F T T T F T T T T T T Hence, it is a tautology. But, the second statement is not a correct explanation for the first.

$p$	$q$	$~ p$	$~ q$	$p \land ~ q$	$~ p \land q$	$(p \land ~ q) \land (~ p \land q)$
$T T F F$	$T F T F$	$F F T T$	$F T F T$	$F T F F$	$F F T F$	$F F F F$

$p$	$q$	$~ p$	$~ q$	$p \to q$	$~ q \to ~ p$	$(p \to q) \leftrightarrow (~ q \to ~ p)$
$T T F F$	$T F T F$	$F F T T$	$F T F T$	$T F T T$	$T F T T$	$T T T T$

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