If A and Bare two events, then the set $A\cap B$ denotes the event

We know that, intersection of two sets $A\cap B$ is the set of those elements which are common to both A and B, i.e., which belong to both 'A and B'.

Thus, $\mathrm{A}\cap \mathrm{B}=\{\omega :\omega \in \mathrm{A}\text{ and }\omega \in \mathrm{B}\}$

For example, in the experiment of 'throwing a die twice' Let A be the event 'score on the first throw is 6' and B is the event 'sum of two scores is atleast 11 '. Then,

$\mathrm{A}=\left\{\right(6,1),(6,2),(6,3),(6,4),(6,5),(6,6\left)\right\}$.

and B = {(5, 6), (6, 5), (6, 6)} 

So, $\mathrm{A}\cap \mathrm{B}=\left\{\right(6,5),(6,6\left)\right\}$