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

$1 \subset A$

Write down all the subsets of the following sets

$\{ 1,2,3\} $

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are

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 $x \in A$ and $A \in B,$ then $x \in B$

Examine whether the following statements are true or false :

$\{ a\} \in \{ a,b,c\} $