Which of the following are sets ? Justify your answer.
The collection of ten most talented writers of India.
The collection of ten most talented writer of India is not a well-defined collection because the criteria for determining a writer's talent vary from person to person.
Hence, this collection is not a set.
Which of the following pairs of sets are equal ? Justify your answer.
$\mathrm{X} ,$ the set of letters in $“\mathrm{ALLOY}"$ and $\mathrm{B} ,$ the set of letters in $“\mathrm{LOYAL}”.$
Write the following sets in the set-builder form :
${\rm{\{ 5,25,125,625\} }}$
Assume that $P(A)=P(B) .$ Show that $A=B$.
$A = \{ x:x \ne x\} $ represents
If $A = \{ 1,\,2,\,3,\,4,\,5\} ,$ then the number of proper subsets of $A$ is