Which of the following binary operations is not commutative?
FURTHER MATHEMATICS
WAEC 2009
Which of the following binary operations is not commutative?
- A. \(a * b = \frac{1}{a} + \frac{1}{b}\)
- B. \(a * b = a + b - ab\)
- C. \(a * b = 2a + 2b + ab\)
- D. \(a * b = a - b + ab\)
Correct Answer: D. \(a * b = a - b + ab\)
Explanation
All other options given are commutative i.e. \(a * b = b * a\), except option D.
\(a * b = a - b + ab\)
\(b * a = b - a + ba\)
\(a - b = -(b - a) \neq b - a\)
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