Q:

True or false:if $A\subset B$, then $P(A)<P(B)$?

They ask me if this statement is true or false, and explain why. They suggest I write an example showing why it is false or true.

The statement is: if $A\subset B$, then $P(A)<P(B)$.

What I tried was to draw a Venn diagram and show that and show that $pa(A)=p(B)$, so then the answer is false. But I want to know if there is a better way to show this, or something a little bit more formal (not too much).
Thanks. 

A:

False: In a normal distribution, $P(\Bbb R)=P(\Bbb R\setminus\{0\})=1$

A:

$$B=A\cup (B-A)\,\,\,,\,\,A\cap (B-A)=\varnothing\quad,P(B-A)\ge 0$$
$$P(B)=P(A)+P(B-A)\implies P(A)\le P(B)$$

