8 Let

Q,Ssube\\\\Omega

such that

Q\\\\cap S!=(O)/()

and suppose

F

is the anallest

\\\\sigma

-al gebra generated by

{Q,S}

. How maxy aets does

F

contain?\ Solution. Let

A=Q-S,B=Q\\\\cap S,C=S-Q,D=(Q\\\\cup S)

. Then

A,B,C,D

is a partition of

\\\\Omega

Therefore,

F

consists of entirdy unions of all combinations of

A,B,C,D

, including themselves and

\\\\Omega

and

(O)/()

. Tha gives us

Z=16

elements, like the cardinal number of the power set of a four-elements set

8 Let Q,S such that QS= and suppose F is the anallest -al gebra generated by {Q,S}. How many sets does F contain? Solution. Let A=QS,B=QS,C=SQ,D=(QS). Then A,B,C,D is a partition of Therefore, F consists of entirely unions of all combinations of A,B,C,D, including themselves and and . Tha gives us Z=16 elements, like the cardinal number of the power set of a four-elements set