Let S = { 1,2,3,...,10}. Suppose M is the set of all the subsets of S, then the relation R = {(A,B) : A cap B neq phi;A,B in M} is:: Relation (Mathematics)

(d): Given, $A \in M \Rightarrow A \cap A = \phi$ , if $A = \phi \\$ So, $R$ is not reflexive. $\\$ If $(A,B) \in R \Rightarrow A \cap B \neq \phi \Rightarrow B \cap A \neq \phi \Rightarrow (B,A) \in R \\$ So, $R$ is symmetric. $\\$ If $(A,B)$ and $(B,C) \in R \Rightarrow A \cap B \neq \phi$ and $B \cap C \neq \phi$ $\\$ $\Rightarrow A \cap C$ is not necessarily non-empty set. Hence, $A \cap C$ not necessarily belongs to $R$ . $\\$ So, $R$ is not a transitive relation. $\\$ $\therefore$ Given relation is symmetric and reflexive only.

Explanation

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

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