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:

$\phi \,....\,B$

Write the set $A = \{ 1,4,9,16,25, \ldots .\} $ in set-builder form.

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

$\varnothing \subset A$

In rule method the null set is represented by

Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.

Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?