JAMB Mathematics 2008 Objective — Question 21
Question 21 of 50 from the Joint Admissions and Matriculation Board (JAMB) Mathematics 2008 Objective paper, with the correct answer and a full explanation.
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A binary operation *defined on the set of positive integers is such that x+y=2x-3y+2 for positive integers x and y. The binary operation
- A. commutative and closed on the set of positive integers
- B. commutative but not closed on the set of positive integersCorrect
- C. neither commutative nor closed on the set of positive integers
- D. not commutative but closed on the set of positive integers
Explanation
x*y=2x-3y+2. y*x=2y-3x+2. Clearly, x*y is not equal to y*x, so the operation is not commutative. Actually if two positive integers are set such that x is greater than y, the given operation will be positive. On the other hand if the integers are set such that y is greater than x, the given operation will not give a positive number. Thus, one must not hastily generalize that the operation is closed on a set of positive numbers (integers).
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