Q5 of 123 Page 3

Define an associative binary operation on a set.

The associative property of binary operations hold if, for a non-empty set A, we can write (a * b) *c = a*(b * c).

Suppose N be the set of natural numbers and multiplication be the binary operation. Let a = 4, b = 5 c = 6. We can write (a × b) × c = 120 = a × (b × c).


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3

Define a binary operation on a set.

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Define a commutative binary operation on a set.

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Write the total number of binary operations on a set consisting of two elements.

 7

Write the identity element for the binary operation * defined on the set R of all real numbers by the rule for all a, b ∈ R.