How many elements has $P(A),$ if $A=\varnothing ?$
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 ${x^2} - 3x + 2 = 0\,\} .$
Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are
If $A = \{ 1,\,2,\,3,\,4,\,5\} ,$ then the number of proper subsets of $A$ is
Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$