question archive Let P(S) be the collection of all subsets of S , and Q(S) be the collection of all proper subsets of S
Let P(S) be the collection of all subsets of S , and Q(S) be the collection of all proper subsets of S
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Let P(S)
be the collection of all subsets of S
, and Q(S)
be the collection of all proper subsets of S
.
Which of the following hold for every set S
?
A) P(S)⊆Q(S)
B) P(S)⊇Q(S)
C) P(S)⊃Q(S)
D) P(S)=Q(S)
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(C) ?P(S)⊃Q(S)?
Step-by-step explanation
The proper subset of the set S is a subset of S that is not equal to S. Therefore Q(S) does not contain S. But P(S) is the collection of all subsets of S . since every set is a subset of itself, S will be contains in P(S).
Therefore ?P(S)⊃Q(S)? is hold for every set S
