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Let w denotes the set of words in the En...

Let w denotes the set of words in the English dictionary. Define the relation R by `R = {(x, y) in W xx W}`, the words x and y have at least one letter in common, then R is

A

not reflexive, symmetric and transitive

B

reflexive, symmetric and not transitive

C

reflexive, not symmetric and transitive

D

reflexive, symmetric and transitive.

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly, (x, x) `in R` for all `x in W`
So, R is reflexive.
Let `(x, y) in R`. Then,
`(x, y) in R`
implies Words x and y have at least one letter in common
implies Words y and x have at least one letter in common
implies `(y,x) in R`
So, R is symmetric.
R is not transitive, because words DELHI and DWARKA, have one letter common. Also, DWARKA and PATNA have one letter common but DELHI and PATNA have no common letter.
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