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 $A \not\subset B$, then $x \in B$
Consider the sets
$\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$
Insert the symbol $\subset$ or $ \not\subset $ between each of the following pair of sets:
$\phi \,....\,B$
Write the following intervals in set-builder form :
$\left( {6,12} \right]$
Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is an even natural mumber $\} \ldots \{ x:x$ is an integer $\} $
Given the sets $A=\{1,3,5\}, B=\{2,4,6\}$ and $C=\{0,2,4,6,8\},$ which of the following may be considered as universal set $(s)$ for all the three sets $A$, $B$ and $C$
$\{ 0,1,2,3,4,5,6\} $