De Morgan's Law - The answer is with square brackets or without square brackets?

by Palillo   Last Updated July 11, 2019 19:20 PM

De Morgan's Law - Propositional Calculus

Can someone tell me what's the correct way to solve this proposition with De Morgan's Law?


q v ¬[ (p ʌ q) v ¬q ]


Option 1:

q v ¬(p ʌ q) ʌ q

Option 2:

q v [¬(p ʌ q) ʌ q ]

As you can see, the difference between both is that one of them don't have square brackets "[ ]". So, what's the correct one?

Answers 1

Because $\vee$ is associative we do not need to distinguish the order of applying the operator. This means the square brackets are superfluous, but they are also acceptable. Either is correct unless your rules of syntax require that all operators come with brackets. That is sometimes done when you want to be very formal.

Ross Millikan
Ross Millikan
July 11, 2019 19:12 PM

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