Given universal set

= ${-6, -5\dfrac{3}{4}, -\sqrt{4}, -\dfrac{3}{5}, -\dfrac{3}{8}, 0, \dfrac{4}{5}, 1, 1\dfrac{2}{3}, \sqrt{8}, 3.01, π, 8.47}$

From the given set, find :

(i) set of rational numbers

(ii) set of irrational numbers

(iii) set of integers

(iv) set of non-negative integers

(i) We need to find the set of rational numbers.

Rational numbers are :

1. Of form $\dfrac{p}{q}$, where q ≠ 0.

2. Integers as well as terminating and recurring decimals are rational numbers.

From the universal set

Set of rational numbers

= ${-6, -5\dfrac{3}{4}, -\sqrt{4}, -\dfrac{3}{5}, -\dfrac{3}{8}, 0, \dfrac{4}{5}, 1, 1\dfrac{2}{3}, 3.01, 8.47}$

(ii) Since,

$\sqrt{8} = 2.82…. \text{ and π} = 3.142….$

Since, the above numbers are neither terminating nor recurring, hence they are irrational.

From the universal set

Set of irrational numbers = ${\sqrt{8}, π}$

(iii) From the universal set

Set of integers = ${-6, -\sqrt{4}, 0, 1}$

(iv) From the universal set

Set of non-negative integers = {0, 1}.