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

Write the following set in the set-builder form: $\{ 3, 6, 9, 12 \}$

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

In this question,all integers are represented in base $10$. Consider the set $E$ of positive integers $n$ having the property that when any nonzero digit $d \in \{1, 2, \dots, 9\}$ is written to the right of $n$,the resulting number is divisible by $d$. Let $N$ be the smallest element of $E$. The product of the digits of $N$ is:

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is a triangle in a plane} } \dots { x:x \text{ is a rectangle in the plane} }$

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