Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to
$25$
$34$
$42$
$41$
$A = \{ x:x \ne x\} $ represents
Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
State whether each of the following set is finite or infinite :
The set of lines which are parallel to the $x\,-$ axis
Which of the following are examples of the null set
$\{ y:y$ is a point common to any two parallellines $\} $
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \subset B$ and $x \notin B,$ then $x \notin A$