A binary operation defines ast on the set of po... - JAMB Mathematics 2008 Question
A binary operation defines \(\ast\) on the set of positive integers is such that x \(\ast\) y = 2x - 3y + 2 for all positive integers x and y. The binary operation is
A
commutative and closed on the set of positive integers
B
neither commutative nor closed on the set of positive integers
C
commutative but not closed on the set of positive integers
D
not commutative but closed on the set of positive integers
correct option: b
a (\ast) b = b (\ast) a
x (\ast) y = y (\ast) x
2x - 3y + 2 (\neq) 2y - 3y - 3x + 2
2 (\ast) 3 = 2(2) -3(3) + 2
= 4 - 9 + 2
= -3
1 (\ast) 2 = 2(1) - 3(2) + 2
= 2 - 6 + 2
= 2 - 6 + 2
= -2
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