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Aug2016 cs Q3

0. Let A and B be sets in a finite universal set U. Given the following: |A – B|, |A ⊕ B|, |A| + |B| and |A ∪ B| Which of the following is in order of increasing size ?

  • Option : D
  • Explanation :
    We will draw venn diagram for all set: |A – B|, |A ⊕ B|, |A| + |B| and |A ∪ B|

    So, option (D) is correct. Alternative way -
    |A – B| = |A| - |A ∩ B|

    |A ⊕ B| = |A| + |B| - 2|A ∩ B|
    |A ∪ B| = |A| + |B| - |A ∩ B|
    Therefore,
    |A – B| < |A ⊕ B| < |A ∪ B| < |A| + |B|
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