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  3. Mathematics
  4. Let X be a non-empty set and P(X) be the set of all subsets of X. For A, B ∈ P(X), A R B if and only if A ∩ B=φ then the relation

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Q. 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 $A \cap B=\phi$ then the relation

Relations and Functions - Part 2

Solution:

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