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Let R and S be two non-void relations on a set A. Which of the

Question

Let $R$ and $S$ be two non-void relations on a set $A$ . Which of the following statements is false?

R

and

S

are transitive implies

R \cap S

is transitive

R

and

S

are transitive implies

R \cup S

is transitive

R

and

S

are symmetric imples

R \cup S

is symmetric

R

and

S

reflexive implies

R \cap S

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Let

R

and

S

be two non-void relations on a set

A

. Which of the following statements is false?

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Let

A = {1, 2, 3}

; R = {(1, 1), (2, 2)}; S = {(2, 2), (2, 3)}

be two transitive relations on

A

Thus

R \cup S = {(1, 1), (1, 2), (2, 2), (2, 3)}

then

(1, 2) \in R \cup S

and

(2, 3) \in R \cup S

but

(1, 3) \in / R \cup S

R \cup S

is not transitive

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Question Text	Let $R$ and $S$ be two non-void relations on a set $A$ . Which of the following statements is false?
Answer Type	Text solution:1
Upvotes	150

Let R and S be two non-void relations on a set A. Which of the following statements is false?

Text solutionVerified

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Let $R$ and $S$ be two non-void relations on a set $A$ . Which of the following statements is false?