Question

a*b = a-b on Q, Examine whether the given binary operations are commutative or not and associative or not.

Answer 1

a * b = a - b.       It is not commutative.       For example,   3*2= 3-2 =1 2*3= 2-3 = -1     2*3 is not equal to 3*2.       Now,        (a*b)*c = (a-b) * c = (a-b)-c = a-b-c.      a*(b*c) = a * (b-c) = a -(b-c) = a -b+c.       a*(b*c) is not equal to (a*b)*c.       Hence * is not associative.