Question
Download Solution PDFLet S be the set of all persons living in Delhi. We say that x, y in S are related if they were born in Delhi on the same day. Which one of the following is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Definition of Equivalence relation
- A relation is an equivalence relation if & only if it is:
- Reflexive property: aRa
- Symmetric property: if a R b, then b R a
- Transitive property: if a R b and b R c, then a R c
Calculation:
Given that,
S = persons living in Delhi x, y ∈ S.
x R y if x & y born on same day.
⇒ First we check reflexive property so,
x R x or y R y both will be reflective.
So reflexive property true for Relation.
⇒ Now symmetric property,
Given that x R y born on same day so it’s reverse y R x also true y and x also born on same day.
Symmetric property also true for relation.
⇒ For transitive property,
Given that x R y born on same day
Let’s take z who also born on same day of y so y R z ∈ S
So we can say that x R z ∈ S because given that x R y and y R z ∈ S.
Transitive property also true for relation.
So this is an equivalence relation.
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