Final answer:
The contrapositive of the statement 'If I live in Montana, then I own a log cabin' is 'If I do not own a log cabin, then I do not live in Montana.'
Step-by-step explanation:
To find the contrapositive of the statement "If I live in Montana, then I own a log cabin," we first identify the components of the conditional statement. The 'if' part is the hypothesis, and the 'then' part is the conclusion. The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion of the original statement and then reversing them.
So, the contrapositive of the original statement is: "If I do not own a log cabin, then I do not live in Montana." This is because the contrapositive inverts and negates both the hypothesis ('I live in Montana') and the conclusion ('I own a log cabin'). Remember, in logic, the contrapositive of a true statement is always true.