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210test1key - Math 2 10 Section O i l Test N AME KEY This...

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NAME: . Math 210 Section O i l : Test KEY This test has 6 pages. The points per page arc 4, 4, 5. 5, 5, 5. [4 points] Question 1. £. ~~ H ~ ~~ ( / Let P be the statement "-4 2 =- 1C." Let, Q be the statement "7 < v'JH). 1 ' Let # be the atatunient "j: - 7 is tlie only solution of (./: - 2) 2 = 25." r-2 =-S x = -3 T
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12 points] Question 2a. Explicitly write out the power set of < a, {b} >. a a [2 points] Question 2b. Let A - {1,2,4,5,0,9}, let B - {1.2.3,5}, and let C~ {5,0,7.8}, Explicitly write out the set (A n C] x (yl n ^).
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[3 points] Question 3a. Construct a Iruth tablo for (P A Q) V ( P P T -T F G T F T F : P -Q F T p-*6fi) F r F T T 1 T P*Q T F F F (NQ)v(py-^)) T T -p / [2 points] Question 3b. If X —*• V is false 1 , find tlir truth value of Tf
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[1 point] Question 4a. Show that the statement /I U (B n (7) - (/I U Z?) n C is false by giving an exp,,c,t conntaoxan.pie [4 points] Question 4b. (,'la.SHify each of the following as true or false. If true, give a. general proof. If false, explicitly give a, specific counterexample. (i) True or false: If A U B = A U C. then B ---- C. (ii) True or false: If An/3 - An C, then B - C. C = ' 3 / 10
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[5 points] Question 5. Define a relation ~ on Z a,s follows: a ~ b if and only
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