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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

Respuesta :

Nirina7
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
I put D and it was correct.

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