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)

$\frac{5}{16}$

Answer 2

The correct answer is (A) : $\frac{5}{16}$
Total number of relations
$=2^{2^2}=2^4=16$
Relations which are symmetric as well as transitive are
φ, {(x, x)}, {(y, y)}, {(x, x), (x, y), (y, y), (y, x)}, {(x, x), (y, y)}
Therefore cases = 5
∴ Probability $= \frac{5}{16}$