Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\varnothing \subset A$

Which of the following is not an example of the null set?

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 $A$ or $B$.

Which of the following are sets? Justify your answer.
$A$ collection of the most dangerous animals of the world.

Let $S = \{1, 2, 3, \ldots, n\}$ and $A = \{(a, b) \mid 1 \leq a, b \leq n\} = S \times S$. $A$ subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S$. Then,the number of good subsets of $A$ is

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