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The relation R defined on the set A={1,\...

The relation `R` defined on the set `A={1,\ 2,\ 3,\ 4,\ 5}` by `R={(a ,\ b):|a^2-b^2|<16}` , is given by {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3) {(2, 2), (3, 2), (4, 2), (2, 4)} {(3, 3), (4, 3), (5, 4), (3, 4) (d) none of these

A

reflexive

B

transitive

C

not symmetric

D

a function

Text Solution

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The correct Answer is:
C
Clearly, (1,1),(2,2),(3,3) and (4,4) are not in R. So, it is not reflexive.
We observe that `(2, 3) in R` but `(3, 2) cancelin R`, it is not symmetric. Clearly, (1, 3) `in R` and `(3, 1) cancelin R " but "(1,1)cancelinR`. So, it is not transitive.
Since (2, 4) and (2, 3) are in R. So, it is not a function. Hence, option (c ) is correct.
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