Question
Given \( n(G)=9, n(H)=15 \), and \( n(G \cap H)=2 \), find \( n(G \cup H) \).
Ask by Hobbs Olson. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( n(G \cup H) = 22 \)
Solution
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Bonus Knowledge
To find \( n(G \cup H) \), we can use the principle of inclusion-exclusion in set theory, which states: \[ n(G \cup H) = n(G) + n(H) - n(G \cap H) \] Substituting the given values into the formula: \[ n(G \cup H) = n(G) + n(H) - n(G \cap H) = 9 + 15 - 2 \] Calculating the right-hand side: \[ n(G \cup H) = 24 - 2 = 22 \] Therefore, the number of elements in the union of sets \( G \) and \( H \) is \( n(G \cup H) = 22 \).
