You must know that $A\subset A$ is always true.
Thus, although an proposition $A$ is false, $A\subset A$ is true.
With similar, if an proposition $A$ is false, then
$A\sim A$ is true.
However, as an proposition $A$ is false,
$A\cdot A$ is false, and
$A\vee A$ is false.
Please check the truth of the proposition "$A\subset (B\vee C)$ ",
where $A$ is false, $B$ is false, and $C$ is false.
If $A$ is "a day has 25 hours ",
$B$ is "a week has 175(=25×7) hours " and
$C$ is "a month has 750(=25×30) hours" , then
"$A\subset (B\vee C)$ " is true .
How do you feel it?
