Question

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
B.
proof by contraposition
C.
proof by law of detachment
D.
proof by theorem

Answer 1

I put D and it was correct.

Answer 2

the answer:
according the statement
"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."
the answerer has just used theorem between combination of ¬p, p, ¬q and q.

that is called theorem of mathematics logic,

so the proof is D. proof by theorem