A binary operation * is defined on the set of positive integers is such x*y = 2x-3y+2 for all positive integers x and y. The binary operation is?
A
commutative and close 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 cummutative but closed on the set of positive integers
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
X * Y = 2X - 3Y + 2
2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer
Source: Myschool Past Questions Archive (Record #9276)