Question

Given universal set =
`{ -6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, sqrt8, 3.01, π, 8.47 }`

From the given set, find: set of rational numbers

Answer 1

Given Universal set is

`{-6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, sqrt8, 3.01, π, 8.47 }`

We need to find the set of rational numbers.

Rational numbers are numbers of the form `P/q`, where q ≠ 0.

U = `{ - 6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, sqrt8, 3.01, π, 8.47 }`

Clearly, `-5 3/4, -3/5, -3/8, 4/5 and 1 2/3  "are of the form"  P/q`.

Hence, they are rational numbers.

Since the set of integers is a subset of rational numbers,

-6, 0 and 1 are also rational numbers.

Thus, decimal numbers 3.01 and 8.47 are also rational numbers.

because they are terminating decimals.

Hence, from the above set, the set of rational numbers is Q, and

Q = `{ - 6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, 3.01, 8.47 }`