First slide

Relations XII

Question

$A s s u m e R a n d S a r e (n o n e m p t y) r e l a t i o n s i n a s e t A . W h i c h o f t h e f o l l o w i n g r e l a t i o n g i v e n b e l o w i s f a l s e$

Moderate

A

$If R and S are transitive, then$ $R \cup S is transitive.$
B

$I f R a n d S a r e t r a n s i t i v e, t h e n$ $R \cap S i s t r a n s i t i v e .$
C

$If R and S are symmetric, then$ $R \cup S is symmetric.$
D

$If R and S are reflexive, Then$ $R \cap S is reflexive.$

Solution

$\begin{array}{l} Consider the example: Let A = {1, 2, 3}, R = {(1, 1), (1, 2)} and S = {(2, 2), (2, 3)} \\ Clearly R and S are transitive relations on A . \\ R \cup S = {(1, 1), (2, 2), (1, 2), (2, 3)} \\ R \cup S is not transitive as (1, 3) \notin R \cup S . \end{array}$

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