Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then
$A$ is always a subset of the complement of $B$
$B$ is always a subset of $A$
$A$ and $B$ are always disjoint
$A$ and the complement of $B$ are always non-disjoint
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 $x \notin A$
Write down all the subsets of the following sets
$\{ a\} $
Which of the following are examples of the null set
$\{ x:x$ is a natural numbers, $x\, < \,5$ and $x\, > \,7\} $
Assume that $P(A)=P(B) .$ Show that $A=B$.
Write the following intervals in set-builder form :
$\left( { - 3,0} \right)$