Q. Which one below is true?

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Every binary operation, on a set satisfies the identity axiom.

Every binary operation, on a set satisfies .

Every commutative binary operation is associative.

Every binary operation defined on a set having exactly one element is both commutative and associative.

Solution:

Addition' is a binary operation on .
Under has no identity element
Under this operation, is an abelian group. 'subtraction' is a binary operation on the set . But .
The operation defined on by is both binary and commutative. But this is not associative (verify this ).

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