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Let A = {p, q, r}. Which of the followin...

Let A = {p, q, r}. Which of the following is an equivalence relation on A?

A

`R_(1) = {(p, q), (q, r), (p, r), (p, p)}`

B

`R_(2) = {(r, q), (r, p), (r, r), (q, q)}`

C

`R_(3) = {(p, p), (q, q), (r, r), (p, q)}`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
D
A = {p, q, r}
`R_(1) = {(p, q), (q, r), (p, r), (p, p)}`
`(q, q) cancelin R_(1)`, so `R_(1)` is not reflexive relation
So, `R_(1)` is not an equivalence relation.
`R_(2) = {(r, q), (r, p), (r, r), (q, q)}`
Here, `(p, p) cancelin R_(2)`, so `R_(2)` is not an equivalence relation .
`R_(3)={(p, p),(q, q), (r, r), (p, q)}`
`R_(3)` is an reflexive relation.
`(p, a) in R_(3) " but "(q, p) cancelinR_(3)`
`R_(3)` is not symmetric relation.
So, `R_(3)` is not equivalence relation.
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