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.

Question

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.

Philoid · Accepted 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.

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b): b = a + 1} is reflexive, symmetric or transitive.