(C) Given $|A| = 3$ and $|B| = 6$. For $A \cup B$,the formula is $|A \cup B| = |A| + |B| - |A \cap B|$. To minimize $|A \cup B|$,we must maximize $|A

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Both statements $(I)$ and $(II)$ are true

(C) Given $|A| = 3$ and $|B| = 6$. For $A \cup B$,the formula is $|A \cup B| = |A| + |B| - |A \cap B|$. To minimize $|A \cup B|$,we must maximize $|A \cap B|$. The maximum value of $|A \cap B|$ is $\min(|A|, |B|) = 3$. Thus,$\min |A \cup B| = 3 + 6 - 3 = 6$. So,Statement $(I)$ is true. For $A \cap B$,the maximum value is $\min(|A|, |B|) = 3$. Thus,$\max |A \cap B| = 3$. So,Statement $(II)$ is true.

Class 11 Mathematics Set Theory Word Problem - Set Theory

Easy

$A$ and $B$ are two sets having $3$ and $6$ elements respectively. Consider the following statements. Statement $(I)$: Minimum number of elements in $A \cup B$ is $6$. Statement $(II)$: Maximum number of elements in $A \cap B$ is $3$. Which of the following is correct?

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A
Statement $(I)$ is true,statement $(II)$ is false
B
Statement $(I)$ is false,statement $(II)$ is true
C
Both statements $(I)$ and $(II)$ are true
D
Both statements $(I)$ and $(II)$ are false

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$A$ and $B$ are two sets having $3$ and $6$ elements respectively. Consider the following statements. Statement $(I)$: Minimum number of elements in $A \cup B$ is $6$. Statement $(II)$: Maximum number of elements in $A \cap B$ is $3$. Which of the following is correct?

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