Write the following as intervals: $\{ x:x \in R, 3 \le x \le 4 \}$

If $A = \{x, y\}$ then the power set of $A$ is

Assume that $P(A) = P(B)$. Show that $A = B$.

The solution set of the congruence $x \equiv 3 \pmod{7}$ is given by:

Write the following interval in set-builder form: $(6, 12]$

Decide,among the following sets,which sets are subsets of one another:
$A = \{ x: x \in \mathbb{R} \text{ and } x \text{ satisfies } x^2 - 8x + 12 = 0 \},$
$B = \{2, 4, 6\}, C = \{2, 4, 6, 8, \dots\}, D = \{6\}$