Question

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

Answer 1

Correct Answer - 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`