A proof of a claim is given below.

Claim: There do not exist integers m and n such that 12m + 15n = 1.

Proof: Suppose such m and n exist. Then 12m + 15n = 3(4m + 5n) = 1. That means 1 is an integer multiple of 3.

That is a contradiction. Determine which of the following is false.

(a) This is a proof by contradiction.

(b) If one more sentence like " Thus ..." is added, it will be a perfect proof.

(c) This is a proof by contraposition.

(d) none of these