Let*be a binary operation on the set Q ofrational numbers as follows:(

1.	Letbe a binary operation on the set Q ofrational numbers as follows:(i) ab =a −b (ii) ab =a2+ b2(iii) ab =a +ab (iv) ab =(a −b)2(v) (vi) ab =ab2Findwhich of the binary operations are commutative and which areassociative.
Answer» Let * be a binary operation on the set Q of rational numbers as follows: (i) a * b = a − b (ii) a * b = a² + b² (iii) a * b = a + ab (iv) a * b = (a − b)² (v) (vi) a * b = ab² Find which of the binary operations are commutative and which are associative.

Letbe a binary operation on the set Q ofrational numbers as follows:(i) ab =a −b (ii) ab =a2+ b2(iii) ab =a +ab (iv) ab =(a −b)2(v) (vi) ab =ab2Findwhich of the binary operations are commutative and which areassociative.

Answer»

Let
*
be a binary operation on the set Q of
rational numbers as follows:

(i) a
*
b =
a −
b (ii) a
*
b =
a²
+ b²

(iii) a
*
b =
a +
ab (iv) a
*
b =
(a −
b)²

(v) (vi) a
*
b =
ab²

Find
which of the binary operations are commutative and which are
associative.