If & represents one of the operations +, - and x. Is (a&b) +

The point here is that the question asks whether \((a@b)+(a@c)=a@(b+c)\) is true FOR ALL NUMBERS a, b, and c?

(1) \(@\) represents subtraction --> the question becomes is \(2a-b-c=a-b-c\), or is \(a=0\)? So \((a@b)+(a@c)=a@(b+c)\) is NOT true for all numbers a, b, and c (so the answer to the question is NO), for this expression to be true \(a\) must equal to zero (so not for all values of \(a\)). Sufficient.

(2) \(m@2\neq{2@}\) --> \(@\) represents subtraction (as it can not be addition or multiplication), so we have the the same info as above. Sufficient.

Answer: D.

Alternately you can see that \((a@b)+(a@c)=a@(b+c)\) to be true FOR ALL NUMBERS a, b, and c then \(@\) must represent multiplication as only for multiplication it's true for all numbers: \(ab+ac=ab+ac\). So the question basically ask whether \(@\) represents multiplication, both (1) and (2) give answer No toth is question.

Hope it's clear.