Q4 of 123 Page 3

Define a commutative binary operation on a set.

A binary operation * on a set A is commutative if a * b = b * a, for all (a, b) ∈ A (non-empty set).


Let addition be the operating binary operation for a = 8 and b = 9, a + b = 17 = b + a.


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2

On the set Z of all integers a binary operation * is defined by a * b = a + b + 2 for all a, b ∈ Z. Write the inverse of 4.

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Define a binary operation on a set.

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Define an associative binary operation on a set.

 6

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