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# 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

Asked by Bhuvan K Iyer 22nd March 2014, 10:37 AM
R = {(x, y): x is the wife of y}
Now,
(x, x) R
Since x cannot be the wife of herself.
R is not reflexive.

Now, let (x, y) R
x is the wife of y.
Clearly y is not the wife of x.
(y, x) R
If x is the wife of y, then y is the husband of x.
R is not transitive.

Let (x, y), (y, z) 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.
(x, z) R
R is not transitive.

Hence, R is neither reflexive, nor symmetric, nor transitive.
Answered by Expert 22nd March 2014, 12:53 PM
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