21 R.2 Sets and Real Numbers Figure 15 shows the relationships among the subsets of the real numbers. As shown, the natural numbers are a subset of the whole numbers, which are a subset of the integers, which are a subset of the rational numbers. The union of the rational numbers and irrational numbers is the set of real numbers. Real Numbers Rational numbers Irrational numbers Integers –11, –6, –3, –2, –1 Whole numbers 0 Natural numbers 1, 2, 3, 4, 5, 37, 40 , – , 4 9 5 8 11 7 Ï2 2Ï8 p 4 p Ï15 Figure 15 R.2 Exercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. Set A is a(n) of set B if every element of set A is also an element of set B. 2. The set of all elements of the universal set U that do not belong to set A is the of set A. 3. The of sets A and B is made up of all the elements belonging to both set A and set B. 4. The of sets A and B is made up of all the elements belonging to set A or to set B (or to both). CONCEPT PREVIEW Work each problem. 5. Identify the set E1, 1 3 , 1 9 , 1 27 , cF as finite or infinite. 6. Use set notation and write the elements belonging to the set 5x x is a natural number less than 66. 7. Let U= 51, 2, 3, 4, 56 and A = 51, 2, 36. Find A′. 8. Find 516, 18, 21, 506¨515, 16, 17, 186. 9. Find 516, 18, 21, 506´515, 16, 17, 186. 10. CONCEPT PREVIEW Match each number from Column I with the letter or letters of the sets of numbers from Column II to which the number belongs. There may be more than one choice, so give all choices. I (a) 0 (b) 34 (c) - 9 4 (d) 236 (e) 213 (f) 2.16 II A. Natural numbers B. Whole numbers C. Integers D. Rational numbers E. Irrational numbers F. Real numbers
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