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8 Let Q,SsubeOmega such that Qcap S!=(O)/() and suppose F is the anallest sigma -al gebra generated by {Q,S} . How maxy aets does F
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
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