/sci/ - Science & Math

>>14888514
Also, how do i eliminate quantifiers when they cant be combined

VxAx v VxAy is not logically equivalent to Vx(Ax v Ay)

i am trying to get Vx(Ax v Ay)

>>14856127
How do i do rule of inference Simplification without using it?

I am trying to prove the conclusion p -> q and i have worked down the hypothesis to:
~r & (~p v q)

I know i have (~p v q) becomes (p -> q) but i want to get rid of r on my own without invoking the rule of inference.

would i do something like this where i introduce my own axiom thing?

~r & (~p v q) & T

i've never introduced anything before like this so im not sure what to do from T.

would i do something like using T like T = (~r v r)?

How do i do rule of inference Simplification without using it?

I am trying to prove the conclusion p -> q and i have worked down the hypothesis to:
~r & (~p v q)

I know i have (~p v q) becomes (p -> q) but i want to get rid of r on my own without invoking the rule of inference.

would i do something like this where i introduce my own axiom thing?

~r & (~p v q) & T

i've never introduced anything before like this so im not sure what to do from T.

would i do something like using T like T = (~r v r)?