Explanation

This question introduces a new definition, but since the definition is either subtraction, division, or multiplication, it's really just a question of symbolism. The caret sign (^) usually represents an exponent, but that's irrelevant here, since we are given a custom definition solely for the purposes of this question.

There are exactly three possible cases in this question: the caret sign means either subtraction, division or multiplication. And looks funny. Is that true for any of these operations? Plugging in numbers, we can convince ourselves that this will be true in general only if the caret sign stands for multiplication. On to the statements, separately first.

Statement (1) says that does not necessarily equal . In mathematical terms, Statement (1) is saying the caret operation is non-distributive, but looking at the statement, we are reminded of multiplication. If did equal , we might be talking about multiplication, but since it's not, then the caret operation is not multiplication. Whether the caret is multiplication is exactly the question we wanted to answer, so we can answer it definitively. Statement (1) is therefore sufficient.

Statement (2), similarly, definitively answers the question of whether the caret symbol is multiplication--it's not. Therefore, Statement (2) is sufficient.

The correct answer is (D).