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Let w denote the words in the english di...

Let w denote the words in the english dictionary. Define the relation R by: R = `{(x,y) in W xx W` | words x and y have at least one letter in common}. Then R is: (1) reflexive, symmetric and not transitive (2) reflexive, symmetric and transitive (3) reflexive, not symmetric and transitive (4) not reflexive, symmetric and transitive

A

not reflexive, symmetric and transitive

B

reflexive, symmetric and not transitive

C

reflexive, symmetric and transitive

D

reflexive, not symmetric and transitive

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly, `(x, x)inR, AAx in W`
So, R is reflexive
Let (x, y) `in R`, then `(y, x) in R` as x and y have atleast one letter in common. So, R is symmetric. But R is not transitive. E.g. Let x = INDIA, y = BOMBAY and z = JUHU
Then, `(x,y)inRand(y,z)inR" but "(x,z)cancelinR`
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