The smallest set $A$ such that $A  \cup  \{1, 2\} = \{1, 2, 3, 5, 9\}$ is

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is

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 ${x^2} - 3x + 2 = 0\,\} .$

Which of the following sets are finite or infinite.

$\{1,2,3, \ldots 99,100\}$

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

$1 \subset A$