The number of relations, defined on the set a,b,c,d, which are both reflexive and symmetri…

Question

The number of relations, defined on the set ${a,b,c,d}$, which are both reflexive and symmetric, is equal to:

Accepted Answer

Number of such relations:

From $A	o A$ such that

$\begin{gathered} n(A)=N \ \Rightarrow {2}^{(\frac{{N}^{2}-N}{2})} \end{gathered}$

for $N=4\Rightarrow {2}^{6}=64$

Alter :

$\begin{gathered} [[|\begin{array}{cccc}0 \quad  - \quad  - \quad  - \ \Theta  \quad  0 \quad  - \quad  - \ \Theta  \quad  \Theta  \quad  0 \quad  - \ \Theta  \quad  \Theta  \quad  \Theta  \quad  0\end{array}]]|\Rightarrow \Theta \ \Rightarrow {2}^{6}=64 \end{gathered}$

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