Which of the following binary operations is cumulative on the set of integers?
- a \(\ast\) b = a + 2b
-
a \(\ast\) b = a + b - ab
- a \(\ast\) b = a2 + b
- a \(\ast\) b = \(\frac{a(b + 1)}{2}\)
The correct answer is: 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.