Unit 11 Exercises

1. List the members of the following sets.

    a) {x | x is a real number such that x= 4}

    b) {x | x is an integer such that x =2}

2. Determine whether each of the following pairs of sets is equal.

  1. {1, 2, 1, 3, 1, 2}, {2, 3, 1}
  2. {{1}}, {1, {1}}
  3.  emptyset.gif (909 bytes), {emptyset.gif 
(909 bytes) }

3. For each of the follwoing sets, determine whether 1 is an element of that set.

  1. {x in.gif (889 bytes) R | x is an integer greater than 1}
  2. {x in.gif (889 bytes) R | x is the square of an integer}
  3. {1, 2, {1}}
  4. {{1}, {{1}}}
  5. {{1, 2}, {1, {1}}}
  6. {{{1}}}

4. Suppose that A, B, and C are sets such that A subseteq.gif 
(874 bytes) B and B subseteq.gif (874 bytes) C. Show that A subseteq.gif (874 bytes) C.

5. Find the power set of each of the following sets.

  1. {a}
  2. {a, {a}}
  3. {emptyset.gif (909 bytes), {emptyset.gif 
(909 bytes) }}

Answer for these exercises