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

$\{\varnothing\} \subset A$

Consider the sets

$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$

Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:

$A \ldots C$

Which of the following pairs of sets are equal ? Justify your answer.

$A = \{ \,n:n \in Z$ and ${n^2}\, \le \,4\,\} $ and $B = \{ \,x:x \in R$ and ${x^2} - 3x + 2 = 0\,\} .$

Examine whether the following statements are true or false :

$\{ x:x$ is an even natural number less than $6\}  \subset \{ x:x$ is a natural mumber which divide $36\} $

Which of the following are sets ? Justify your answer.

The collection of questions in this chapter.

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If $A \subset B$ and $B \in C,$ then $A \in C$