List all the elements of the following set:
$F = \{ x : x \text{ is a consonant in the English alphabet which precedes } k \}$

Show that $A \cup B = A \cap B$ implies $A = B$.

If $aN = \{ ax : x \in N \}$,then the set $3N \cap 7N$ is equal to $kN$,where $k$ is:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $B$ or $C$.

Which of the following is an example of the null set?
$\{ x : x \in \mathbb{N}, x < 5 \text{ and } x > 7 \}$

Find the pairs of equal sets,if any,give reasons:
$A = \{ 0 \}$
$B = \{ x : x > 15 \text{ and } x < 5 \}$
$C = \{ x : x - 5 = 0 \}$
$D = \{ x : x^2 = 25 \}$
$E = \{ x : x \text{ is an integral positive root of the equation } x^2 - 2x - 15 = 0 \}$