We consider the relation ๐ ={(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐)}.Isย ๐ transitive? Justify briefly
Question
We consider the relation R = {(a, a), (a, b), (a, c), (a, d), (a, e), (b, c), (b, e), (d, a), (e, c)}. Is R transitive? Justify briefly.
Solution
A relation R on a set A is said to be transitive if for every a, b, c in A, whenever (a, b) and (b, c) are in R, then (a, c) is also in R.
Let's check the given relation R = {(a,a),(a,b),(a,c),(a,d),(a,e),(b,c),(b,e),(d,a),(e,c)} for transitivity.
We can see that (a, b) and (b, c) are in R, and (a, c) is also in R. Similarly, (a, d) and (d, a) are in R, and (a, a) is also in R.
However, we have (d, a) and (a, b) in R, but (d, b) is not in R. Similarly, we have (b, e) and (e, c) in R, but (b, c) is not in R.
Therefore, the relation R is not transitive.
Similar Questions
We consider the relation ๐ ={(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐),(๐,๐)}.Isย ๐ transitive? Justify briefly
A={1,2,3,4}, THEN R={(1,2),(1,3),(3,3),(3,1)} IS A __________ans.TRANSITIVE RELATIONNON SYMMETRIC RELATIONANTI SYMMETRIC RELATIONREFLEXIVE RELATION
Q1. Let ๐ด = {0,1,2,3,4,5,6,7} suppose ๐ ๐๐๐ ๐ are two relations on ๐ด such that ๐ = {(๐ฅ, ๐ฆ): ๐ฅ + 2๐ฆ โฅ 4}, ๐ = {(๐ฅ, ๐ฆ): 2๐ฅ + 3๐ฆ โ ๐ด} Write ๐ , ๐, ๐๐๐ ๐ ยฐ๐
If ๐ (๐ฅ, ๐ฆ) = โ๐ฅ ๐๐๐๐๐๐ ๐ข๐๐๐ ๐ฆ, โ express the following in unambiguousEnglish:a. โ๐ฅ โ๐ฆ ๐ (๐ฅ, ๐ฆ)b. โ๐ฆ โ๐ฅ ๐ (๐ฅ, ๐ฆ)c. โ๐ฅ โ๐ฆ ๐ (๐ฅ, ๐ฆ)
Find the transitive closure of the relation)}1,4(),4,3(),3,2(),2,1{(๏ฝR . ShowiR for allvalues ofi that give new elements of the transitive closure
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.