Write the solution set of the equation $x^2 + x - 2 = 0$ in roster form.

What is the remainder when the polynomial $P(x) = 1 + x + x^3 + x^9 + x^{27} + x^{81} + x^{243}$ is divided by $x - 1$?

In the following,state whether $A = B$ or not:
$A = \{ x: x \text{ is a multiple of } 10 \}$
$B = \{ 10, 15, 20, 25, 30, \ldots \}$

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $x \in A$ and $A \not\subset B$,then $x \in B$

Find the union of each of the following pairs of sets:
$A = \{1, 2, 3\}, B = \varnothing$

Write down all the subsets of the following set: $\{a\}$