**Unit 11 Exercises**

**1. **List the members of the following sets.

a) {*x* | *x* is a real number such that *x*²= 4}

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

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

- {1, 2, 1, 3, 1, 2}, {2, 3, 1}
- {{1}}, {1, {1}}
- , { }

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

- {
*x***R**|*x*is an integer greater than 1} - {
*x***R**|*x*is the square of an integer} - {1, 2, {1}}
- {{1}, {{1}}}
- {{1, 2}, {1, {1}}}
- {{{1}}}

**4.** Suppose that *A*, *B*, and *C* are sets such
that *A* *B* and *B*
*C*. Show that *A*
*C*.

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

- {a}
- {a, {a}}
- {, { }}