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Exercises for CS1512 Week 12 Sets (questions)

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1.List the members of these sets: a.{x | x is an integer x >0 x<12} b.{x | x is the square of an integer and x<100} c.{x | x is an integer such that x 2 = 2} 2.For each of the following sets, determine whether 2 is an element of that set a.{2,{3}} b.{{2},{2,{2}}} c.{{{2}}} 3.Give the cardinality of the sets in questions 1 and 2.

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4. Which of the following statements are true? a.1 {0,1,2,3} b.{0,1,2} {0,1,2,3} c.{0,1,2} {0,1,2,3} d.0 e.{0} f.{ } { } g. { } 5. Suppose A B and B C. Prove or disprove a.A C. b.A B C c.C D D d.C P(C)

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4. Translate into English and determine the truth value of each of the following: (R is the set of real numbers.) R(x 2 x) a. x R(x 2 x) R(x 2 -1) b. x R(x 2 -1) c. x R(x 2 x) d. xR y R(y=x+1) d. x R y R(y=x+1) e. xR y R(y=x 2 ) e. x R y R(y=x 2 )

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5. This exercise explores Russells paradox. First some easy bits: a.Is it true that {a} {a}? Why (not)? b.Define S={x|x {a,b,c}}. What is S? c.Define T={a,b,c,d,e}. What is {x T|x {a,b,c}}. Now for the hard part: d. Define V={x|x x}. Is V V? Why (not)? e. Define W={x|x x}. Is W W? Why (not)?

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