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Question: The contrapositive of \((p \vee q) \Rightarrow r\) is...

The contrapositive of (p∨q)⇒r(p \vee q) \Rightarrow r is

A

r⇒(p∨q)r \Rightarrow (p \vee q)

B

∼r⇒(p∨q)\sim r \Rightarrow (p \vee q)

C

∼r⇒ 6mu∼p 6mu∧∼q\sim r \Rightarrow \mspace{6mu}\sim p\mspace{6mu} \land \sim q

D

p⇒(q∨r)p \Rightarrow (q \vee r)

Answer

∼r⇒ 6mu∼p 6mu∧∼q\sim r \Rightarrow \mspace{6mu}\sim p\mspace{6mu} \land \sim q

Explanation

Solution

Contrapositive of p⇒qp \Rightarrow q is ∼q⇒ 6mu∼p\sim q \Rightarrow \mspace{6mu}\sim p

∴ contrapositive of (p∨q)⇒r(p \vee q) \Rightarrow r is

∼r⇒ 6mu∼(p∨q)\sim r \Rightarrow \mspace{6mu}\sim(p \vee q) i.e. ∼r⇒(∼p 6mu∧∼q)\sim r \Rightarrow (\sim p\mspace{6mu} \land \sim q).