Let E F and G be three sets State expressions for the events

Let E, F and G be three sets. State expressions for the events:

only F occurs

exactly two of the events occur

plz explain ur answer

Solution

Only F occurs :

E u F u G - E - G

Explanation : EuFuG is the part tha is all of the circles. From this, i remove E and G,
so only F remains.

Exactly two of the events occur :

(E n F) + (E n G) + (F n G) - 2*(E n F n G) ---> required expression

Explanation :

EnF is the part common to only E and F AND (all E,F and G)
EnG is the part common to only E and G and (all E,F and G)
FnG is the part common to only F and G and (all E,F and G)
Since when all those were added, the (all E,F and G) was added thrice, i subtracted 2*(E n F n G) to get the required expression