If R and S are transitive relations on a set A, then prove that R∪S may not be transitive relation on A.

Let A={a,b,c}then R={(a,a),(a,b),(b,a),(b,b)}and S={(b,b),(b,c),(c,b),(c,c)} be transitiveNow, (a,b)∈R∪SAlso,(b,c)∈R∪SBut (a,c)∈/S∪S∴R∪S is not transitive.

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If R and S are transitive relations on a set A, then prove tha

Question

If $R$ and $S$ are transitive relations on a set $A$ , then prove that $R \cup S$ may not be transitive relation on $A$ .

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Mila Discussed

R

and

S

are transitive relations on a set

A

, then prove that

R \cup S

may not be transitive relation on

A

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Let

A = {a, b, c}

then

R = {(a, a), (a, b), (b, a), (b, b)}

and

S = {(b, b), (b, c), (c, b), (c, c)}

be transitive

Now,

(a, b) \in R \cup S

Also,

(b, c) \in R \cup S

But

(a, c) \in / S \cup S

∴ R \cup S

is not transitive.

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Question Text	If $R$ and $S$ are transitive relations on a set $A$ , then prove that $R \cup S$ may not be transitive relation on $A$ .
Answer Type	Text solution:1
Upvotes	150

If R and S are transitive relations on a set A, then prove that R∪S may not be transitive relation on A.

Text solutionVerified

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If $R$ and $S$ are transitive relations on a set $A$ , then prove that $R \cup S$ may not be transitive relation on $A$ .