Question

Subject: discrete mathematics - sets and logic.

Determine whether the following argument is valid:

Some computers have great processors. For some computer x, if x has a great processor, then x can run Photoshop. Therefore, some computer can run photoshop. Justify your response.

Answer 1

The argument is Valid.

Valid arguments are ones such that if the premises are true, then it is 100% certain that the conclusion is true.

Consider two premises P1 and P2 such that,

P1:Some computers have great proffessors.

P2:For some computer x, if x has a great processor, then x can run Photoshop.

And

C:Therefore some computer can run photoshop.

Here C denotes the conclusion.

Here if P1 and P2 both are true then C must be true.Because if C is false then it means no computer can run photoshop.It means No computer have great proffessors.This implies that P1 is false.But we assumed that P1 is true.Hence Contradiction.

So C must be true.

Hence The argument is VALID.