Determine whether the following relation is transitive or not: R={(x,y):y=x+5 and x<4} ? R={(1,6),(2,7),(3,8)}

Asked by Koushtav Chakrabarty | 29th Mar, 2013, 12:59: PM

Expert Answer:

R = {(x, y): y = x + 5 and x < 4} = {(1, 6), (2, 7), (3, 8)}

Observe that there is no pair in R such that (x, y) and (y, z) belongs R so (x, z) cannot belong to R. Therefore, R is not transitive.

 
Now, whether to convert the given set into roaster form depends upon the question which is asked. Like in the above question, you can very easily determine that the relation is not transitive by quickly converting it into roaster form.

Answered by  | 30th Mar, 2013, 10:59: PM

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