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Exercises for CS1512 Week 12 Sets (questions)

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**List the members of these sets:**

{x | x is an integer x >0 x<12} {x | x is the square of an integer and x<100} {x | x is an integer such that x2 = 2} For each of the following sets, determine whether 2 is an element of that set {2,{3}} {{2},{2,{2}}} {{{2}}} Give the cardinality of the sets in questions 1 and 2.

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**4. Which of the following statements are true?**

1{0,1,2,3} {0,1,2}{0,1,2,3} {0,1,2}{0,1,2,3} 0 {0} {} {} {} 5. Suppose AB and BC. Prove or disprove AC. ABC CDD 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.) xR(x2x) xR(x2-1) xR(x2x) xRyR(y=x+1) xRyR(y=x2)

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**5. This exercise explores Russell’s paradox. First some easy bits:**

Is it true that {a}{a}? Why (not)? Define S={x|x{a,b,c}}. What is S? Define T={a,b,c,d,e}. What is {xT|x{a,b,c}}. Now for the hard part: d. Define V={x|xx}. Is VV? Why (not)? e. Define W={x|xx}. Is WW? Why (not)?

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DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

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