please explain the question in the attached picture.
CB
$\displaystyle (A \cap B) \cup (A-(A \cap B)) = A$
Because :$\displaystyle (A \cap B) and (A-(A \cap B)) $ are mutually exclusive .
$\displaystyle So , P((A \cap B) \cup A-(A \cap B)) = P(A \cap B) + P(A-(A \cap B)) = P(A) $
and , $\displaystyle P(X) >= 0 $, with every events .
Therefore , $\displaystyle P(A \cap B) =< P(A)$