Question
Sat March 22, 2014 By: Bhuvan K Iyer

relation R in set A of human beings in a town at a particular time given by R={(x,y):x is wife of y } pls explain how this relation Is transitive

Expert Reply
Sat March 22, 2014
R = {(x, y): x is the wife of y}
Now,
(x, x) not an element of R
Since x cannot be the wife of herself.
rightwards double arrowR is not reflexive.

Now, let (x, y) element of R 
rightwards double arrow x is the wife of y.
Clearly y is not the wife of x.
rightwards double arrow(y, x) not an element of R
If x is the wife of y, then y is the husband of x.
rightwards double arrowR is not transitive.
 
Let (x, y), (y, z) element of R
? x is the wife of y and y is the wife of z.
This case is not possible. Also, this does not imply that x is the wife of z.
rightwards double arrow(x, z) not an element of R
rightwards double arrowR is not transitive.

Hence, R is neither reflexive, nor symmetric, nor transitive.
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