Which of the following are sets ? Justify your answer.
The collection of all natural numbers less than $100 .$
The collection of all natural numbers less than $100$ is a well-defined collection because one can definitely identify a number that belongs to this collection.
Hence, this collection is a set.
Write down all the subsets of the following sets
$\{ 1,2,3\} $
If $A = \{ 1,\,2,\,3,\,4,\,5\} ,$ then the number of proper subsets of $A$ is
Write the following sets in roster form :
$C = \{ x:x{\rm{ }}$ is a two-digit natural number such that sum of its digits is $8\} $
Write the following intervals in set-builder form :
$\left( { - 3,0} \right)$
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:
$\phi \,....\,B$