Find detailed and accurate answers to your questions on IDNLearn.com. Get accurate and timely answers to your queries from our extensive network of experienced professionals.
Sagot :
To find the value of [tex]\( n(A \cup B) \)[/tex], we use the principle of inclusion-exclusion for two sets. This principle states that for any two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex],
[tex]\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \][/tex]
Given the problem, we have:
- [tex]\( n(A) = 7 \)[/tex]
- [tex]\( n(B) = 12 \)[/tex]
- [tex]\( n(A \cap B) = 5 \)[/tex]
We can now substitute these values into the formula:
[tex]\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \][/tex]
Substituting the given values, we get:
[tex]\[ n(A \cup B) = 7 + 12 - 5 \][/tex]
Performing the addition and subtraction within the equation:
[tex]\[ 7 + 12 = 19 \][/tex]
[tex]\[ 19 - 5 = 14 \][/tex]
Thus, the value of [tex]\( n(A \cup B) \)[/tex] is [tex]\( 14 \)[/tex].
So the final answer is:
[tex]\[ n(A \cup B) = 14 \][/tex]
Therefore, [tex]\( n(A \cup B) = 14 \)[/tex].
[tex]\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \][/tex]
Given the problem, we have:
- [tex]\( n(A) = 7 \)[/tex]
- [tex]\( n(B) = 12 \)[/tex]
- [tex]\( n(A \cap B) = 5 \)[/tex]
We can now substitute these values into the formula:
[tex]\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \][/tex]
Substituting the given values, we get:
[tex]\[ n(A \cup B) = 7 + 12 - 5 \][/tex]
Performing the addition and subtraction within the equation:
[tex]\[ 7 + 12 = 19 \][/tex]
[tex]\[ 19 - 5 = 14 \][/tex]
Thus, the value of [tex]\( n(A \cup B) \)[/tex] is [tex]\( 14 \)[/tex].
So the final answer is:
[tex]\[ n(A \cup B) = 14 \][/tex]
Therefore, [tex]\( n(A \cup B) = 14 \)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.