#### Answer

a) Natural Numbers: 8, 13
b) Whole Numbers: 0, 8, 13
c) Integers: -9, 0, 8, 13
d) Rational Numbers: -9, -0.7, 0, $\frac{6}{7}$, 4.666..., 8, $\frac{21}{2}$, 13, $\frac{75}{5}$
e) Irrational Numbers: -$\sqrt 6$, $\sqrt7$

#### Work Step by Step

a) Natural Numbers: 8, 13
(The set of Natural Numbers includes {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ...})
b) Whole Numbers: 0, 8, 13
(The set of Whole Numbers includes {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ...})
c) Integers: -9, 0, 8, 13
(The set of Integers includes {...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...})
d) Rational Numbers: -9, -0.7, 0, $\frac{6}{7}$, 4.666..., 8, $\frac{21}{2}$, 13, $\frac{75}{5}$
(The set of Rational Numbers are all numbers that can be written in fractional form. This includes Natural Numbers, Whole Numbers, fractions, and repeating decimals using repetends)
e) Irrational Numbers: -$\sqrt 6$, $\sqrt7$
(The set of Irrational Numbers are all numbers that cannot be written in fractional form. This will include square roots that are not perfect squares.)