October 29, 2023
October 29, 2023
October 29, 2023
UGC NET CS 2016 Aug- paper-2
October 29, 2023

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 ?

Correct Answer: D

Question 3 Explanation:
Step-1: Let A and B be sets in a finite universal set U.
Step-2: |A–B| we can also write into |A|-|A ∩ B| and equivalent Venn diagram is

Step-3: |A⊕B| We can also write into |A|+|B|- 2|A∩B| and equivalent Venn diagram is

Step-4: |A| + |B| We can represented into |A| + |B| and equivalent Venn diagram is

Step-5: |A∪B| We can also write into |A|+|B|- |A∩B| and equivalent Venn diagram is

Step-6: |A – B| ≤ |A ⊕ B| ≤ |A ∪ B| ≤ |A| + |B| is correct order.
|A – B| ≤ |A ⊕ B| ≤ |A| + |B| ≤ |A ∪ B|
|A ⊕ B| ≤ |A – B| ≤ |A ∪ B| ≤ |A| + |B|
|A ⊕ B| ≤ |A| + |B| ≤ |A – B| ≤ |A ∪ B|
|A – B| ≤ |A ⊕ B| ≤ |A ∪ B| ≤ |A| + |B|
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