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##### IST230 Lesson 7 quiz

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solution

**Question**

Question;1. (Counts Double);Let;A be the set of all students who enjoy solving puzzles;Let;B be the set of all students who do well in IST 230;Now;use the following ?facts? to give a formal proof that A = B (Hint: remember you;must prove two separate things). The ?facts? are;(1) If a student is a good;problem solver, then the student does well in IST 230;(2) If a student enjoys;solving puzzles, then the student is a good problem solver;(3) If a student does well in;IST 230, then the student is a good problem solver;(4) If a student is a good;problem solver, then the student enjoys solving puzzles;2. Give the definition and a;concrete example of a proper subset;3. Let A be the set of all integers;x such that x is = k2 for some integer k;Let B be the set of all integers x such that the square;root of x, SQRT(x), is an integer;Give a formal proof that A = B. Remember;you must prove two things: (1) if x is in A, then x is in B, AND (2) if x is in B, then x is in A;4. Explain when two sets are;disjoint and give a concrete example;Tell;whether or not the following are equal. Explain your answers. HINT: look;carefully at the notations used;5. {1, 2, 1, 3} = {3, 2, 1};6. (1, 2, 1, 3) = (3, 2, 1);7. (1, 2, 1, 3) = (1, 2, 3, 1);Let;A = {5, 6} B = {g, h, i} C = {a, b};8.;Calculate A;x B x C =;Let A = {1, 2, x} B = {d, e, f} C = {2, x, y} U = {1, 2, d, e, f, x, y};9.;Calculate A;? C =;10.;Calculate A;? B =;11.;Calculate A;? C =;12.;Calculate CC (the set complement of C) =;13. Give an example of a partition;of set U

Paper#61049 | Written in 18-Jul-2015

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