Associativity, huh ?

Logic Level 2

If P , Q , R P, Q , R are propositional variables, is [ ( P ⇒ Q ) ⇒ R ] [(P \Rightarrow Q) \Rightarrow R] equivalent to [ P ⇒ ( Q ⇒ R ) ] [P \Rightarrow (Q \Rightarrow R)] ?

No Yes

Venkata Karthik Bandaru by Venkata Karthik Bandaru , 20, India

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1 solution

Consider the case where P , Q P, Q and R R are assigned truth value false. Then, [ ( P ⇒ Q ) ⇒ R ] [(P \Rightarrow Q) \Rightarrow R] is false, whereas [ P ⇒ ( Q ⇒ R ) ] [P \Rightarrow (Q \Rightarrow R)] is true. Hence, both are not equivalent.

Note : If you are unfamiliar with propositional logic, do take time to read this .

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Moderator note:

In general, it's very unlikely that a mere rearranging of parenthesis would result in a true statement. We need to apply one of the rules, which results in the terms moving about, or having to consider the complement.

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