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 $x \notin A$
True
Let $A \subset B$ and $x \notin B$
To show: $x \notin A$
If possible, suppose $x \in A$
Then, $x \in B,$ which is a contradiction as $x \notin B$
$\therefore x \notin A$
State whether each of the following set is finite or infinite :
The set of numbers which are multiple of $5$
Examine whether the following statements are true or false :
$\{ a,b\} \not\subset \{ b,c,a\} $
The number of proper subsets of the set $\{1, 2, 3\}$ is
Which of the following sets are finite or infinite.
$\{1,2,3, \ldots 99,100\}$
Which of the following are examples of the null set
$\{ y:y$ is a point common to any two parallellines $\} $