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 = \(\frac{a(b + 1)}{2}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(a \ast b = a + b - ab\)
\(b \ast a = b + a - ba\)
On the set of integers, the two above are cumulative as multiplication and addition are cumulative on the set of integers.
Source: Myschool Past Questions Archive (Record #30916)