Sets Relations And Functions Question 57
Question: Let R and S be two non-void relations on a set A. Which of the following statements is false
Options:
A) R and S are transitive $ \Rightarrow R\cup S $ is transitive
B) R and S are transitive $ \Rightarrow R\cap S $ is transitive
C) R and S are symmetric $ \Rightarrow R\cup S $ is symmetric
D) R and S are reflexive $ \Rightarrow R\cap S $ is reflexive
Show Answer
Answer:
Correct Answer: A
Solution:
- Let $ A={1,,2,,3} $ and R = {(1, 1), (1, 2)}, S = {(2, 2) (2, 3)} be transitive relations on A. Then R U S = {(1, 1); (1, 2); (2, 2); (2, 3)} Obviously, R U S is not transitive. Since (1, 2) $ \in $ R U S and $ (2,,3)\in R\cup S $ but (1, 3) $ \notin R\cup S $ .
BETA
