(i) 2*5 = 3(2)+5 = 11.
(ii) x*y = 3x+y but y*x = 3y+x thus * is not commutative since
for all values of x and y.(iii) If x*y = x then 3x+y = x i.e.
QUESTION
* is a binary operation on the integers Z where x*y
= 3x+y.
(i) Evaluate 2*5
(ii) Is * a commutative operation on Z?
(iii) If x*y = x, write y in terms of x.
ANSWER
(i) 2*5 = 3(2)+5 = 11.
(ii) x*y = 3x+y but y*x = 3y+x
thus * is not commutative since
for all values of x and y.
(iii) If x*y = x then 3x+y = x i.e.