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R(2) on Q defined by (a,b)inR(2) iff a...

`R_(2)` on Q defined by `(a,b)inR_(2) iff ab=4` Relation `R_(2)` is

A

reflexive

B

symmetric

C

transitive

D

equivalence

Text Solution

Verified by Experts

The correct Answer is:
B
We have (a, b) `in R_(2)` iff ab = 4, where a, b `in` Q
Reflexivity `5 in Q` and (5)(5) = `25 ne 4`
`therefore (5, 5) cancelin R_(2)`
The relation `R_(2)` is not reflexive.
Symmetry
(a, b) `in R_(2)`
`implies ab = 4 implies ba = 4`
`implies (b, a) in R_(2)`
`therefore` The relation `R_(2)` is symmetric.
Transitivity We have `(8,(1)/(2)),((1)/(2),8)inR_(2)` because
`8((1)/(2))=4 and ((1)/(2))(8)=4`
Also, 8(8) = 64 `ne` 4
`therefore (8, 8) cancelin R_(2)`
`therefore` The relation `R_(2)` is not transitive.
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