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 integers C. neither commutative nor closed on the set of positive integers D. not commutative but closed on the set of positive integers
- 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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