Question

(Is my answer correct? ) Given: p is true
Prove: p → q is true
Assume p and ~q are both true. ~q → r, and r → ~p. Therefore, ~p and p cannot be true, so p and ~q cannot be true. Therefore, p → q is true.

What type of proof is illustrated above?

A.proof by contradiction
C.proof by law of detachment
D.proof by theorem

Answer 1

I think its law of detachement

Answer 2

something has to be missing

why are they throwing r in there?

Answer 3

is this the full proof?

Answer 4

In logic, the law of detachment works with the statement "P implies Q". The law basically states that if you know the first part is true (P), then Q must be true.

Syllogism works with the statements "P implies Q" and "Q implies R" (notice Q is mentioned twice). If both those statements are true, then the statement "P implies R" is true.

Answer 5

Yes.

Answer 6

well they point out that "~p and p cannot be true", so that's a contradiction

Answer 7

but this proof is just bizarre to be honest, not sure how they got what they got

Answer 8

So it should be proof by contradiction?

Answer 9

it's like they're making a lot of jumps

Answer 10

I think so

Answer 11

ok. thanks for your input.(:

Answer 12

besides, proof by law of detachment is a bit more straight forward than what they're saying

so that's why I think we can eliminate it

Answer 13

Hmm..Sounds right. But i couldnt really understand this problem either.