Hello, I am looking at a problem in Philosophy, and more specifically Logic with a double turnstile.

The problem is as follows: True or false? Prove that your answer is correct. If α |= γ or β |= γ, then
α ∨ β |= γ

I know you use the a and B and y to represent formulas, but can you let them represent any formula? And if so how would you go about starting this problem?

Would you simply create a truth table with a b and a v b?

Any help would be appreciated.

a v b to mean "a and b" ?

a v b means a or b. not exactly sure what the question is.
it seems just by definition that ~a and ~b implies ~(a or b )
is that what ur needing to prove?

This post was edited by hellomoto13 on Oct 22 2013 10:54pm

what does the vertical line | mean?

im assuming he means =/= (not equal to)

ahh, if that's the case, then it's DeMorgan's Laws.
Just make a truth table and show both are equivalent

~a v ~b <--> ~(a ^ b )

truth table this and show both sides are equivalent

This post was edited by TritonV8 on Oct 22 2013 11:01pm

the |= is a term called a turnstile, where if you read a |= b, it means b is provable from a. So the question is if Y is provable from a, and Y is provable from B, is Y therefore provable from A or B? If so how.

The A, B, and Y each representing individual formulas, not just letters

This post was edited by OAcquaintanceO on Oct 22 2013 11:06pm

i've never encountered a turnstile. But logically, if it is provable from function A or B separately, then it will be provable from A v B