Final answer:
The contrapositive of the statement "if X, then Y" is "if not Y, then not X." The correct contrapositive, given the options, is (a) y → ¬x.
Step-by-step explanation:
The contrapositive of a conditional statement of the form "if X, then Y" is "if not Y, then not X." The contrapositive always has the truth value equivalent to the original statement, regardless of the actual content of X and Y. Given the statement x → y, the contrapositive would be not y → not x (if not Y, then not X).
To determine the correct answer from the provided options, the contrapositive must negate both the hypothesis (X) and the conclusion (Y) and also reverse their order. Therefore, the statement "if not Y, then not X" is the correct contrapositive of the statement "if X, then Y". Hence, the correct answer is (a) y → ¬x, which expresses "if not y, then not x" in symbolic form.
It is important to avoid confusing the contrapositive with the converse or the inverse. The converse would be "if Y, then X" and the inverse would be "if not X, then not Y"; neither of these necessarily has the same truth value as the original statement.