State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $(x - 1)(x - 2) = 0\} $

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

$1 \subset A$

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

$\{1,2,5\}\in A$

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ 2,3,4\}  \ldots \{ 1,2,3,4,5\} $

Are the following pair of sets equal ? Give reasons.

$A = \{ 2,3\} ,\quad \,\,\,B = \{ x:x$ is solution of ${x^2} + 5x + 6 = 0\} $

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 $x \in B$