Let
A and
B be two subsets of
S . There are following cases to make a subset of
S, under the given condition i.e.
A∪B=S and
A∩B=ϕ Case I : If set
A has no element. The number of ways of selection of 0 element from set
S is
nC0 .
Case II : If set A has one element. The number of ways of selection of one element from set
S is
nC1 .
Case III : If set A has two elements. The number of ways of selection of two element from set
S is
nC2 .
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Case
(n) : If set
A has
n elements. The number of ways of selection of
n elements from set
S is "
nCn .
∴ Total set of
A=nC0+nC1+nC2+.....+nCn =2n Total set of
A arid
B=2n×2n=22n Required probability
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