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Consider the following relation on subsets of the set ? 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?

Consider the following relation on subsets of the set ? 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? Correct Answer Both S1 and S2 are true

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.

Since: S = {1, 2, 3, ...., 2014}.

Therefore, Subsets {1, 2, 3, …., 2014} and {Ø} of S, so {1, 2, 3, …., 2014} < {Ø} because the minimum element in the symmetric difference (i.e., {1, 2, 3, ...., 2014}) of the two sets is in set {1, 2, 3, ...., 2014}.

Hence, {Ø} is a subset of S that is larger than every other subset. And, {1, 2, 3, …., 2014} is a subset of S that is smaller than every other subset.

Hence, {Ø} is a subset of S that is larger than every other subset.

And, {1, 2, 3, …., 2014} is a subset of S that is smaller than every other subset.

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