CODEWITHSUNDEEP
mathlogical-operatorsoperation
user4780686
user4780686

Reputation:

Logical Equivalence Law for Removing Parentheses

I have a problem problem such as:

¬P ∨ (Q ∨ R)

I used the law that :

¬P ∨ (Q ∨ R) ≡ ¬P ∨ Q ∨ R

But I do not remember the name of the law. Can anybody help me?

Upvotes: 1

Views: 1733

Answers (1)

John Coleman
John Coleman

Reputation: 52008

You are thinking of the associative law, but there is a subtlety:

What the associative law says is that

P v (Q v R) = (P v Q) v R

Depending on your formal system of logic, there is a good chance that 

P v Q v R

isn't officially a wff (well-formed formula) since it is syntactically ambiguous. The associative law guarantees that both ways of parsing it are equivalent, hence it is a common abbreviation for (P v Q) v R.

Thus, I would tend to regard

P v (Q v R) = P v Q v R

as giving an abbreviation which is underwritten by the associative law rather than as an application of the associative law per se.

Upvotes: 1

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