Exercises for CS1512 Week 12 Sets (questions)

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.

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 AB and BC. Prove or disprove AC. ABC CDD C  P(C)

4. Translate into English and determine the truth value of each of the following: (R is the set of real numbers.) xR(x2x) xR(x2-1) xR(x2x) xRyR(y=x+1) xRyR(y=x2)

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 {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)?