JCBNLA Posts: 5, Reputation: 1 New Member #1 May 13, 2022, 05:38 AM
Symbolic Logic Question
In propositional logic, the disjunction "P or Q", symbolized as "P v Q" can be taken to be "inclusive" or "exclusive." Inclusive would mean "P or Q or both", whereas exclusive would mean "P or Q but not both."

It is the convention among logicians that a disjunction is to be taken as inclusive, and not exclusive. My understanding is that the reason inclusive was chosen over exclusive is that the exclusive disjunction makes working with logic more cumbersome.

My question is this: Besides making logic more cumbersome, is there something illogical about the exclusive disjunction? The truth table says that if both disjuncts are true, then the disjunction as a whole is false--because, by definition, only one of the disjuncts can be true in an exclusive disjunction. But consider this disjunction: the number 7 is prime or the number 7 is odd. Both disjuncts are true, but it seems absurd to say both disjuncts taken together is false.
 Wondergirl Posts: 39,354, Reputation: 5431 Jobs & Parenting Expert #2 May 13, 2022, 08:38 AM
How would you symbolize that (7 prime,7 odd)?
 JCBNLA Posts: 5, Reputation: 1 New Member #3 May 16, 2022, 03:56 AM
One way to symbolize it is "P or O"

P = the number 7 is prime
O = the number 7 is odd

Since my original post I've already discovered the answer to my question.
 Wondergirl Posts: 39,354, Reputation: 5431 Jobs & Parenting Expert #4 May 16, 2022, 09:09 AM
I'm glad you figured it out!

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