1. **State the problem:** We need to classify the numbers in set A = { -6, \frac{1}{2}, -1.333... (3's repeat), \pi, 2, 5 } into (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, and (e) Real numbers. 2. **Recall definitions:** - Natural numbers: positive integers starting from 1 (1, 2, 3, ...). - Integers: whole numbers including negatives, zero, and positives (..., -2, -1, 0, 1, 2, ...). - Rational numbers: numbers that can be expressed as a fraction \frac{p}{q} where p and q are integers and q \neq 0. - Irrational numbers: numbers that cannot be expressed as a fraction, their decimal expansions are non-repeating and non-terminating. - Real numbers: all rational and irrational numbers. 3. **Analyze each element:** - -6: integer, rational, real (not natural because negative). - \frac{1}{2}: rational, real (not integer or natural). - -1.333... (3's repeat): repeating decimal, equals -\frac{4}{3}, rational, integer? No, natural? No. - \pi: irrational, real. - 2: natural, integer, rational, real. - 5: natural, integer, rational, real. 4. **Classify sets:** (a) Natural numbers: $\{2, 5\}$ (b) Integers: $\{-6, 2, 5\}$ (c) Rational numbers: $\{-6, \frac{1}{2}, -\frac{4}{3}, 2, 5\}$ (d) Irrational numbers: $\{\pi\}$ (e) Real numbers: all elements $\{-6, \frac{1}{2}, -\frac{4}{3}, \pi, 2, 5\}$ **Final answer:** (a) $\{2, 5\}$ (b) $\{-6, 2, 5\}$ (c) $\{-6, \frac{1}{2}, -\frac{4}{3}, 2, 5\}$ (d) $\{\pi\}$ (e) $\{-6, \frac{1}{2}, -\frac{4}{3}, \pi, 2, 5\}$