Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:
S1: There is a subset of S that is larger than every other subset. S2: There is a subset of S that is smaller than every other subset.
Which one of the following is CORRECT?
(A)
Both S1 and S2 are true
(B)
S1 is true and S2 is false
(C)
S2 is true and S1 is false
(D)
Neither S1 nor S2 is true
Answer: (A)
Explanation:
According to the given information :
S1 is true because NULL set is smaller than every other set.
S2 is true because the UNIVERSAL set {1, 2, …, 2014} is larger than every other set.
Thus, both S1 and S2 are true.
Quiz of this Question
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