Let S={1,2,3, ldots, 10}. Suppose M is the se | vedclass

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Question

Let $S=\{1,2,3, \ldots, 10\}$

$R=\{(A, B): A \cap B 
eq \phi ; A, B \in M\}$

For Reflexive,

$M$ is subset of ' $S$ '

So $\phi \in

Vedclass · Accepted Answer

symmetric only

Vedclass · Answer

Let $S=\{1,2,3, \ldots, 10\}$

$R=\{(A, B): A \cap B 
eq \phi ; A, B \in M\}$

For Reflexive,

$M$ is subset of ' $S$ '

So $\phi \in \mathrm{M}$

for $\phi \cap \phi=\phi$

$\Rightarrow$ but relation is $\mathrm{A} \cap \mathrm{B} 
eq \phi$

So it is not reflexive.

For symmetric,

$\mathrm{ARB}$

$\mathrm{A} \cap \mathrm{B} 
eq \phi,$

$\Rightarrow \mathrm{BRA} \quad \Rightarrow \mathrm{B} \cap \mathrm{A} 
eq \phi$,

So it is symmetric.

For transitive,

If $\mathrm{A}=\{(1,2),(2,3)\}$

$ B=\{(2,3),(3,4)\} $

$C=\{(3,4),(5,6)\}$

$ARB$ $BRC$ but $A$ does not relate to $C$

So it not transitive

Let $S=\{1,2,3, \ldots, 10\}$. 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 :

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