Q50

MCQ2 marks, −0.67

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 $\text{CORRECT}$ ?

(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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