The following table defines an operation * on the set A={a, b} * a b
a b b
b. a a
a. find a*b, b*a, a*a
b. is*a binary operation. why?
c. As per the definition of binary operation it is a function .Write its domain and co- domain.
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(a) If I'm reading the table correctly, by definition of *, we have

a * a = b

a * b = b

b * a = a

b * b = a

(b) Yes, * is a binary operation. A binary operation is a function * that maps elements from A × A to A, where

A × A = {{a, b} | a ∈ A and b ∈ A}

In this case,

A × A = {{a, a}, {a, b}, {b, a}, {b, b}}

and * is defined such that each of these pairs gets mapped to either a or b, both elements of A. In other words, A is closed under *.

(c) The domain is A × A and the co-domain is A.

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