Which of the following binary operations is cumulative on the set of integers?
-
A.
a (ast) b = a + 2b -
B.
a (ast) b = a + b – ab -
C.
a (ast) b = a2 + b -
D.
a (ast) b = (frac{a(b + 1)}{2})
Correct Answer: Option B
Explanation
(a ast b = a + b – ab)
(b ast a = b + a – ba)
On the set of integers, the two above are cumulative as multiplication and addition are cumulative on the set of integers.