Question

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to ______.

Options

• `5/16`

• `9/16`

• `11/16`

• `13/16`

Answer 1

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to `underlinebb(5/16)`.

Explanation:

Let set p = {x, y}

∵ = {x, y}

⇒ p × Q = {(x, x), (x, y}, (y, x), (y, y)}

So, total number of relations from p to Q = 2⁴ = 16

Now, relations which are symmetric as well as transitive are `phi`, {x, x}, {(y, y}, {(x, x), (y, y)}, {(x, x), (x, y), (y, y), (y, x)}

∴ Favourable case = 5

As we know by the classic definition of probability, the probability of an event is the ratio of the number of cases favourable to it, to the number of total possible cases.

∴ Required probability = `5/16`