relation r in the set N of natural no. defined as R={(x,y):y=x+5 and x<4} is it transitive

Asked by  | 7th Jul, 2009, 03:36: PM

Expert Answer:

Relation R in the set N of natural no. R={(x,y):y=x+5 and x<4}

In Roster Form R = {(1,6),(2,7),(3,8)}

Now clearly R is not reflexive since none of the ordered pairs (1,1),(2,2),....etc are inR
Similarly (1,6) is in R but (6,1) is not so it is not symmetric.But it is transitive since there are no ordered pairs of the form
(a,b), (b,c) in R for that (a,c) is not in R .

There are no ordered pairs in R which voilets the definition
So R istransitive.

 

Answered by  | 9th Jul, 2009, 08:55: AM

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