Let E, F, and G be three events. Find expressions for the following events: a. Non of them occur. b. Both E and G occur but F does not occur. c. only E occur.

a. (E U F U G)'

b. E n F (G') or EF(G')

c. E n (F U G)' or E(F U G)'

Step-by-step explanation:

The three events are E, F, G

For this question, we'll make use of set notations

U -> Union

Example is A U B which means an occurrence that happens in either A or B

n -> Intersection

Example is A n B which means an occurrence that happens in A and B.

It can also be written as AB

' -> Complement

Example is A' which means an event where A doesn't occur.

So, we'll move to the questions

a. None of them occur.

This means that;

E doesn't occur

F doesn't occur

G doesn't occur.

So, the notation is (E U F U G)'

b. Both E and F occur but G doesn't occur

This mean that

E and F occur

G didn't occur.

The notation is E n F (G') or EF(G')

c. Only E occur

This means that E occur

And Either F or G didn't occur

The notation is, E n (F U G)' or E(F U G)'

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.