Questions
Let R and S be two non-void relations on a set A. Which of the following statements is false
a
R and S are transitive ⇒R∪S is transitive
b
R and S are transitive ⇒R∩S is transitive
c
R and S are symmetric ⇒R∪S is symmetric
d
R and S are reflexive ⇒R∩S is reflexive
detailed solution
Correct option is C
Let A=1, 2, 3 and R=1, 1, 1, 2, S=2, 22, 3be transitive relations on A.Then R∪S=1, 1; 1, 2; 2, 2; 2, 3Obviously, R∪S is not transitive. Since 1, 2∈R∪S and 2, 3∈R∪S but 1, 3∉R∪S.Talk to our academic expert!
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