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Anti symmetric relation: Definition...

Anti symmetric relation: Definition

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What is Anti Symmetric Relation: Definition

Here, we will study about Antisymmetric Relation. In Mathematics, your teacher might have given you to work on a mathematical concept called relations. A relation is a set of ordered pairs, (x, y), where x is related to y by some rule.

Consider the relation 'is divisible by' over the integers. Call it relation R. This relation would consist of ordered pairs, (x,y), such that x and y are integers, and x is divisible by y. Now, consider the teacher's facts again. By fact 1, the ordered pair (number of cookies, number of students) would be in R, and by fact 2, the ordered pair (number of students, number of cookies) would also be in R.

Relations seem pretty straightforward. Let's take things a step further. You see, relations can have certain properties and this lesson is interested in relations that are antisymmetric. An antisymmetric relation satisfies the following property:

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