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 are sets ? Justify your answer.

The collection of all natural numbers less than $100 .$

Examine whether the following statements are true or false :

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

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

$\{1,2,3\}\subset A$

Write down all the subsets of the following sets

$\emptyset $

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