Question

Hi brainlies!!
Q. What are symmetric relations of sets? (no spam)​

Answer 1

Answer:

Here we will discuss about the symmetric relation on set.

Let A be a set in which the relation R defined. Then R is said to be a symmetric relation, if (a, b) ∈ R ⇒ (b, a) ∈ R, that is, aRb ⇒ bRa for all (a, b) ∈ R.

Consider, for example, the set A of natural numbers. If a relation A be defined by “x + y = 5”, then this relation is symmetric in A, for

a + b = 5 ⇒ b + a = 5

But in the set A of natural numbers if the relation R be defined as ‘x is a divisor of y’, then the relation R is not symmetric as 3R9 does not imply 9R3; for, 3 divides 9 but 9 does not divide 3.

For a symmetric relation R, R−1 = R.

Answer 2

Step-by-step explanation:

Symmetric Relation: A relation R on a set A is called symmetric if (b,a) € R holds when (a,b) € R.i.e. The relation R={(4,5),(5,4),(6,5),(5,6)} on set A={4,5,6} is symmetric. AntiSymmetric Relation: A relation R on a set A is called antisymmetric if (a,b)€ R and (b,a) € R then a = b is called antisymmetric.