Q20 State whether the following statements are true or false. Justify.

1. For an arbitrary binary * on N, a *a = a, for all a∈N
2. If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a
3. Every binary operation defined on a set having exactly one element a is necessarily commutative and associative with a as the identity element and a being the inverse of a

Solution

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