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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 7

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Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasing size ?

  1. $|A-B|<|A \oplus B|<|A|+|B|<|A \cup B|$
  2. $|A \oplus B|<|A-B|<|A \cup B|<|A|+|B|$
  3. $|A \oplus B|<|A|+|B|<|A-B|<|A \cup B|$
  4. $|A-B|<|A \oplus B|<|A \cup B|<|A|+|B|$
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Take example, A={1,2,3} and B={2,3,4}

|A−B| = |{1}| = 1

$\left | A\oplus B \right |$ = |{1,4}| = 2

$\left | A\cup B \right |$ = |{1,2,3,4}| = 4.

|A| + |B| = 3+3 = 6

Correct Option: D

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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 10
Which of the following statements is $\textbf{FALSE}$? $C-(B \cup A)=(C-B)-A$ $A-(C \cup B)=(A-B)-C$ $B-(A \cup C)=(B-C)-A$ $A-(B \cup C)=(B-C)-A$
Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$$A-(C \cup B)=(A-B)-C$$B-(A \cup C)=(B-C)-A$$A-(B \cup C)=(B-C)-A$
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