Question

Let s={1,2,3} define the relaltion p={(1,1),(1,2),(2,2),(1,3),(3,1),(3,3),(2,1)} check whether it is 1)reflexive 2)symmetric 3)transitive 4)equivalence

Answer 1

Answer:

S ={1,2,3}

P ={(1,1),(1,2),(2,2),(1,3),(3,1),(3,3),(2,1)}

1. Since (1,1),(2,2), (3,3) ∈ P

So P is reflexive

2. Since for every (x,y) ∈ P implies ( y, x ) ∈ P

So P is symmetric

3. Since for every (x,y) ∈ P, (y,z) ∈ P implies (x,z) ∈ P

So P is transitive

4. Since P is Reflexive, Symmetric Transitive

Hence P is a Equivalence Relation

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