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Unit 2 Assignment 1 Intersections and Types of Numbers 1: Draw the venn diagram of the number system. Then place the following numbers in the correct position –1, 1, π, 7 , 3.333 3 , 3 16 . 2: Let U = {–4, – (a) (c) 3: 2 33 , 1, π, 13, 26.7, 69, 10 }. A is set of integers in U. B is set of rational numbers in U. 3 List all the prime numbers contained in U. List all the members of B. (a) (b) (d) List all the members of A. List all the members of the set A B. 4 Given w = 4.3 x 10-3 x = 2.6 × 10 and y = , which of the following statements about the nature of x, y and w below are incorrect? (Circle your answers) (i) x y (ii) w < y (iii) (iv) x + y (v) y 1 < x (vii) x y w (vi) (vii) w + x 4: Explain why the number 2π must be irrational, given that π is irrational. 5: Complete the table below, showing which of the number sets these numbers belong to: Natural Whole Integer Rational Irrational Real 5 0.5 5 –5 5√3 ∗ 2√3 5√3 + 2√3 (4-√3)(4 + √3) 6√2 − 3√8 7: Name the groups that ¾ belongs to 8: Name the groups that 3 doesn’t belong to 9: Let A = {Odd numbers from 1-99}. Find set B so that A B = 10: Consider a right triangle with legs a=5 and b=7 and hypotenuse of c. Determine if the following are true or false: (a) a*b is a natural number (b) a – c is a rational number (c) c2 is an integer (d) b2 – c2 is a whole number 11: Let A ε {A,B,C,D,E,F,G,H) Let B ε {5 Vowels of the alphabet}. Find the following: (a) A U B (b) A B 12: A set of numbers is considered closed if the operation of the set with itself will yield only that set. For example, integers are closed under multiplication because an integer * integer will always be an integer but not closed under division because 7/0 isn’t an integer. Determine if the following are closed or not. Give an example if it is not closed. (a) Natural numbers under subtraction (b) Irrational numbers under addition (c) Real number under division.