Question

show that the relation in the set {1,2,3} given by R={(1,2) (2,1)} Is symmetric but reflexive nor transitive​

Answer 1

Answer:

• We observe that (1, 1), (2, 2) and (3, 3) do not belong to R. So, R is not reflexive .
• Clearly, (1, 2) ∈ R and (2, 1) ∈ R. So, R is symmetric.
• As (1, 2) ∈ R and (2, 1) ∈ R but (1, 1) ∉ R. So, R is not transitive.

Condition For reflexive

• In Maths, a binary relation R across a set X is reflexive if each element of set X is related or linked to itself.
• In terms of relations, this can be defined as (a, a) ∈ R ∀ a ∈ X or as I ⊆ R where I is the identity relation on A. Thus, it has a reflexive property and is said to hold reflexivity

Condition for symmetric

• Symmetric relation is the relationship between two or more elements such that if the first element is associated with the second then the second element is also linked to the first element in a similar fashion.
• (a,b) ∈ R ⇒ (b,a) ∈ R for all a, b ∈ A.
• aRb ⇒ bRa for all a,b ∈ A.

Condition for transitive

• In Mathematics, a transitive relation is defined as a homogeneous relation R over the set A, where the set contains the elements such as x, y and z, such that R relates x to y and y to z, then R also relates x to z.
• Mathematically, we can address it as a relation R marked on a set A is a transitive relation: If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈R.for all a, b, c ∈ A.

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