For each of the following pairs of sets $A, B$, determine if $A\subset B$ or $A\not\subset B$ :

$A=\{x:x$ is an odd integer$\}$,

$B=\{x:x$ is real and not an even integer$\}$

For each of the following pairs of sets $A, B$, determine if $A\subset B$ or $A\not\subset B$ :

$A=\{x:x$ is an integer which is both even and odd$\}$,

$B=\{x:x$ is an integer and $x\ne x\}$

For following pair of sets $A, B$, determine if $A\subset B$ or $A\not\subset B$ :

$A=\{a,b,c\}, B=\left\{\right\{a\},\{b\},\{c\left\}\right\}$

$\{1,2\}\notin \{1,2,3\}$

$A\subset A$ for any set $A$

Every set has a proper subset.

Every set is a proper subset of the same set.

For any object $x$, there is a set $A$ such that $x\in A$.

For every object $x$, there is a set $A$ such that, $x\notin A$.