If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ .
A)75
B) 65
C) 5
D) 150
E) 10

Name: If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ . A)75 B) 65 C) 5 D) 150 E) 10
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Question

If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ .  
A)75
B) 65
C) 5
D) 150
E) 10

Quizplus · Accepted Answer

Using the principle of inclusion-exclusion, we have $n(A \cup B) = n(A) + n(B) - n(A \cap B)$. Substituting the given values, we get $140 = 75 + 75 - n(A \cap B)$, which simplifies to $n(A \cap B) = 150 - 140 = 10$.

If n(A∪B)=140n ( A \cup B ) = 140n(A∪B)=140 And n(A)=n(B)=75n ( A ) = n ( B ) = 75n(A)=n(B)=75

If $n ( A \cup B ) = 140$ And $n ( A ) = n ( B ) = 75$