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 $A \not\subset B$ and $B \not\subset C,$ then $A \not\subset C$
False
Let $A=\{1,2\}, B=\{0,6,8\},$ and $C=\{0,1,2,6,9\}$
Accordingly, $A \not\subset B$ and $B \not\subset C$.
However, $A \not\subset C$
$A = \{ x:x \ne x\} $ represents
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$ 5\, .......\, A$
The number of proper subsets of the set $\{1, 2, 3\}$ is
Write the following intervals in set-builder form :
$\left( {6,12} \right]$
State whether each of the following set is finite or infinite :
The set of lines which are parallel to the $x\,-$ axis