. symmetric relation definition


Best Answer

A binary relation R described on a set A is called to be symmetric if, for elements a, b ∈ A, we have aRb, that is, (a, b) ∈ R, then we need to have bRa, that is, (b, a) ∈ R. This means that a relation defined on a set A is a symmetric relation if and only if it satisfies aRb ⇔ bRa for all elements a, b in A. If there's a single ordered pair in R such that (a, b) ∈ R and (b, a) ∉ R, then R isn't a symmetric relation.

Example :

♦ 'Is same to' is a symmetric relation described on a set A as if an detail a = b, then b = a. aRb ⇒ a = b ⇒ b = a ⇒ bRa, for all a ∈ A

♦ 'Is similar to' is a symmetric relation on a set of numbers as a is similar to b if and only if b is similar to a.

♦ 'Is a biological sibling' is a symmetric relation as though one person A is a biological sibling of some other person B, then B is likewise a biological sibling of A.

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