Consider the following relation on subsets of the set ܵ$S$ of integers…

GATE · 2014 · CS · Set 2 · Computer Science & IT

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

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Consider the following relation on subsets of the set ܵ\(S\) of integers…