1.3.5 Let A, B, and C be three events. Match, where possible, events D1 through Dlo with events El through Ell. Matching means that the events are exactly the same; that is, if one occurs, so must the other and conversely (see the Definition 1.3.2). (Hint: Draw a Venn diagram for each event D1,. . . , D10, do the same for events E l , . . . ,Ell, and then compare the diagrams.)

Among events A, B, C:

D1 = two or more occur.

D2 = exactly one occurs.

0 3 = only A occurs.

0 4 = all occur.

D5 = none occurs.

D6 = at most one occurs.

D7 = at least one occurs.

0 8 = exactly two occur.

Dg = no more than two occur.

Dlo = B occurs.

El=AUBUC.

E3 = ( A n B)" n ( A n C)" n ( B n C)", E4 = ( A U B U C)".

& = A n B n c .

E7 = B.

E8 = A f l BC n C".

Ez = ( A nB Cn Cc)u ( A C nB nCc)u ( A c nB Cn C).

E~ = A" n B" n cc.

E9 = ( A n B n Cc )u ( A n B Cn c)u (ACn B n C) .

El0 = ( A n B n C)".

El1 = ( A n B) u ( A n C ) u (B n C ) .