Relation

The noun relation appears to be one of those slippery words that resists explanation.

Our strategy will be to group together, here, things called relations.

The symbol \in[\latex] is a relation. It is sometimes called "Set Membership".

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A relation between two sets is a collection of ordered pairs containing an object from each set.

Let A={1,2,3,4} and B={2,4,6,8} and let the relation between A and B be the ordered pairs shown below:

• (1,2)
• (2,4)
• (3,6)
• (4,8)

In the above we have a relation from set A to set B. We can give that relation the symbol, R, and then write 1R2, 2R4, 3R6, 4R8.

The R can be replaced by commonly used symbols such as <, =, >.

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