1. Exercises for CS1512 Week 12
Sets
(questions)

2. 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.

3. 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. 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. 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)?