First slide

Relations XII

Question

Let S be the set of all subsets of first 10 natural numbers. If a relation R is defined on set S such that (A, B) $\in$ R if $A \cap B \neq ϕ; w h e r e A, B \in S$ , then R is

Moderate

A

Symmetric and Transitive only
B

Symmetric and reflexive only
C

Symmetric only
D

Reflexive only

Solution

$ϕ \cap ϕ = ϕ \Rightarrow (ϕ, ϕ) \notin R$
$∴$ R is not reflexive
Clearly R is symmetric but not transitive $(i f A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6} t h e n A \cap B = {3} \neq \emptyset a n d B \cap C \neq \emptyset b u t A \cap C = \emptyset . s o n o t t r a n s i t i v e)$

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