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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.

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Solution

Let A={1,2,3,4,5,6}.
A relative R is defined on set A as:
R={(a,b):b=a+1}
R={(1,2),(2,3),(3,4),(4,5),(5,6)}
We can find (a,a)R, where aA.
For instance, (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)R
R is not reflexive.
It can be observed that (1,2)R, but (2,1)R.
R is not symmetric.
Now, (1,2),(2,3)R
But, (1,3)R
R is not transitive.
Hence, R is neither reflexive, nor symmetric, nor transitive.

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