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GATE 2014 CS (CS2) – Question 60

Engineering Mathematics · Discrete Mathematics: Sets, Relations, Functions, Partial Orders and Lattices · 2 marks · Multiple choice

S is the set of integers from 1 to 2014. For distinct subsets U,V, define U < V when the minimum element of their symmetric difference belongs to U. S1: A subset of S is larger than every other subset. S2: A subset of S is smaller than every other subset. Which is correct?

  1. Both S1 and S2 true
  2. S1 true, S2 false
  3. S2 true, S1 false
  4. Neither true

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Correct answer: (A) Both S1 and S2 true

Explanation

For any nonempty U, the smallest element of its symmetric difference with∅lies in U, so U<∅; the empty set is largest. For any proper V⊂S, the minimum of S△Vlies in S, so S<V; the full set is smallest. Thus **both statements true,A**.