Question

What type of a relation is R where
R = {(2, 2), (3, 3), (2, 3), (3, 2), (3, 1), (2, 1) } on the set
A={1, 2, 3} ?
(a) reflexive
(b) symmetric
(c) equivalence relation (d) transitive​

Answer 1

Answer:

B . reflexive

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Answer 2

Answer:

c) equivalent relation

Step-by-step explanation:

Given Relation

R={,(2,2),(3,3),(4,4)...}

Reflexive: If a relation has {(a,b)} as its element, then it should also have {(a,a),(b,b)} as its elements too.

Symmetric: If a relation has (a,b) as its element, then it should also have {(b,a)} as its element too.

Transitive: If a relation has {(a,b),(b,c)} as its elements, then it should also have {(a,c)} as its element too.

Now, the given relation satisfies all these three properties.

Therefore, its an equivalence relation.