Question
Given \( n(G)=9, n(H)=15 \), and \( n(G \cap H)=2 \), find \( n(G \cup H) \)
Ask by Potter Cox. in the United States
Mar 17,2025
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Tutor-Verified Answer
Answer
\( n(G \cup H) = 22 \)
Solution
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Mind Expander
To find \( n(G \cup H) \), you can use the principle of inclusion-exclusion, which states: \[ n(G \cup H) = n(G) + n(H) - n(G \cap H) \] Now, substituting the given values: \[ n(G \cup H) = n(G) + n(H) - n(G \cap H) = 9 + 15 - 2 \] Calculating this gives: \[ n(G \cup H) = 24 - 2 = 22 \] So, \( n(G \cup H) = 22 \).
