For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?

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 $x \in A$ and $A \in B,$ then $x \in B$

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to

Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:

$ 8\, .......\, A $

Write the following as intervals :

 $\{ x:x \in R, - 4\, < \,x\, \le \,6\} $

Write the following sets in roster form :

$\mathrm{F} =$ The set of all letters in the word $\mathrm{BETTER}$