Q. 34.2( 75 Votes )
Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
Answer :
Let us take A = {1, 2, 3, 4, 5, 6}
A relation R is defined on set A as:
R = {(a, b): b = a + 1}
Then, R = {(1,2), (2,3), (3,4), (4,5), (5,6)}
Now, we will find (a, a) ∉ R, where a ϵ A
For instance,
(1,1), (2,2), (3,3), (4,4), (5,5), (6,6) ∉ R
Therefore, R is not reflexive.
We can see that (1,2) ϵ R, but (2,1) ∉ R.
Therefore, R is not symmetric.
And now, (1,2), (2,3) ϵ R
But, (1,3) ∉ R
Therefore, R is not transitive.
Therefore, R is neither reflexive, nor symmetric, nor transitive.
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