First slide

Relations XII

Question

Let $X$ be a non-empty set and $P (X)$ be the set of all subsets of $X$ . For $A, B \in P (X), A R B$ if and only if $A \cap B = \emptyset$ then the relation

Moderate

A

$R$ is reflexive
B

$R$ is symmetric
C

$R$ is transitive
D

$R$ is an equivalence relation

Solution

$A \cap A = A \neq ϕ$ if $A \neq ϕ,$ So $R$ is not reflexive.
$A \cap B = \emptyset \Rightarrow B \cap A = \emptyset$
$A R B \Rightarrow B R A \Rightarrow R$ is symmetric
Note $R$ is not transitive and not an equivalence relation.

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