If p , q and r are three propositions, then which of the following combination of truth values of p , q and r makes the logical expression { ( p ∨ q ) ∧ ( ( ~ p ) ∨ r ) } → ( ( ~ q ) ∨ r ) false ?

Question

If p , q and r are three propositions, then which of the following combination of truth values of p , q and r makes the logical expression { ( p ∨ q ) ∧ ( ( ~ p ) ∨ r ) } → ( ( ~ q ) ∨ r ) false ?, p = T , q = F , r = T, p = T , q = T , r = F, p = F , q = T , r = F, p = T , q = F , r = F

MARKS App · Accepted Answer

Given, { ( p ∨ q ) ∧ ( ( ~ p ) ∨ r ) } → ( ( ~ q ) ∨ r ) Now solving the above expression using truth table from given options we get, p q r p ∨ q ~ p ∨ r A ≡ p ∨ q ∧ ~ p ∨ r B ≡ ~ q ∨ r A → B A T F T T T T T T B T T F T F F F T C F T F T T T F F D T F F T F F T T So, only Option C will be false.

	$p$	$q$	$r$	$(p \lor q)$	$(~ p \lor r)$	$A \equiv (p \lor q) \land (~ p \lor r)$	$B \equiv ~ q \lor r$	$A \to B$
$(A)$	T	F	T	T	T	T	T	T
$(B)$	T	T	F	T	F	F	F	T
$(C)$	F	T	F	T	T	T	F	F
$(D)$	T	F	F	T	F	F	T	T

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