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Define a binary operation on a set.

Binary operations on a set are calculations that combine two elements of the set (called operands) to produce another element of the same set.

The binary operations * on a non-empty set A are functions from A × A to A. The binary operation, *: A × A → A. It is an operation of two elements of the set whose domains and co-domain are in the same set.


More from this chapter

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1

Write the identity element for the binary operation * on the set R0 of all non-zero real numbers by the rule for all a, b ∈ R0.

 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.

 4

Define a commutative binary operation on a set.

 5

Define an associative binary operation on a set.