Question

The probability that a relation $R$ from $\{x,y\}$ to $\{x,y\}$ is both symmetric and transitive, is equal to:

• A. $\frac{5}{16}$
• B. $\frac{9}{16}$
• C. $\frac{11}{16}$
• D. $\frac{13}{16}$

Answer 1

Answer: (A)

Total no. of relations $=2^{2\times 2}=16$
Fav. relation $=\varphi ,\{(x,x)\},\{(y,y)\},\{(x,x)(y,y)\}$
$\{(x,x),(y,y),(x,y)(y,x)\}$
Prob. $=\frac{5}{16}$