Question

Fill in the following table so that the binary operation * on A = {a, b, c} is commutative.

*	a	b	c
a	b
b	c	b	a
c	a		c

Answer 1

Given that the binary operation * is Commutative.

To find a * b:

a * b = b * a   ........(∵ * is a Commutative)

Here b * a = c.

So a * b = c

To find a * c:

*	a	b	c
a	b	c	a
b	c	b	a
c	a	a	c

a * c = c * a  ........(∵ * is a Commutative)

c * a = a.  .......(Given)

So a * c = a

To find c * b:

c * b = b * c

Here b * c = a.

So c * b = a