Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
Let $X$ be the set of letters in $"CATARACT".$ Then
$X=\{ C , A , T , R \}$
Let $Y$ be the set of letters in $"TRACT".$ Then
$Y=\{T, R, A, C, T\}=\{T, R, A, C\}$
Since every element in $X$ is in $Y$ and every element in $Y$ is in $X$. It follows that $X = Y$.
List all the elements of the following sers :
$F = \{ x:x$ is a consonant in the Englishalphabet which precedes $k\} $
State whether each of the following set is finite or infinite :
The set of numbers which are multiple of $5$
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$ 8\, .......\, A $
What universal set $(s)$ would you propose for each of the following :
The set of right triangles
Write the following as intervals :
$\{ x:x \in R, - 4\, < \,x\, \le \,6\} $