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Which of the following binary operations is cumulative on the set of integers?

Mathematics
JAMB 1995

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 = \(\frac{a(b + 1)}{2}\)
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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.

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