Let A and B be sets in a finite universal set U. Given the following :
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?
Show answerHide answer
Correct answer: (D) |A – B| ≤ |A ⊕ B| ≤ |A ∪ B| ≤ |A| + |B|
Explanation
Using a Venn diagram: A – B ⊆ A ⊕ B ⊆ A ∪ B, and |A ∪ B| = |A| + |B| – |A ∩ B| ≤ |A| + |B|. Therefore |A – B| ≤ |A ⊕ B| ≤ |A ∪ B| ≤ |A| + |B|.