Determine which of the following binary operations are assoc

Determine which of the following binary operations are associative. The operation on Z defined b = a - b. The operation on R defined b = a + b + ab. The operation on Q defined b = a + b/5. The operation on Z Times Z defined by (a_1b_1) (a_2, b_2) = (a_1b_2) = (a_1b_2 + b_1a_2, b_1b_2). The operation on Q {0} defined by a b =

Solution

Associaive property is valid with addition and multiplication but not with division because cahnge in parenthesis for diviion changes the result.

thus 1 , 2 and 4 are associative and rest are not