Question

State the closure property of addition. Give an example to verify the statement.

Answer 1

Step-by-step explanation:

A set that is closed under an operation or collection of operations is said to satisfy a "closure property." Often a closure property is introduced as an axiom, which is then usually called the axiom of closure. Modern set-theoretic definitions usually define operations as maps between sets, so adding closure to a structure as an axiom is superfluous; however in practice operations are often defined initially on a superset of the set in question and a closure proof is required to establish that the operation applied to pairs from that set only produces members of that set.

For example :

the set of even integers is closed under addition, but the set of odd integers is not.

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