Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To find \( n(X \cup Y) \), the number of elements in the union of the sets \( X \) and \( Y \), we will use the principle of inclusion-exclusion for sets. The formula for the union of two finite sets is given by:
[tex]\[ n(X \cup Y) = n(X) + n(Y) - n(X \cap Y) \][/tex]
Here, \( n(X) \) represents the number of elements in set \( X \), \( n(Y) \) represents the number of elements in set \( Y \), and \( n(X \cap Y) \) represents the number of elements that are common to both sets \( X \) and \( Y \).
Given the values:
- \( n(X) = 12 \)
- \( n(Y) = 19 \)
- \( n(X \cap Y) = 7 \)
We substitute these values into the formula:
[tex]\[ n(X \cup Y) = 12 + 19 - 7 \][/tex]
Perform the arithmetic operations:
[tex]\[ n(X \cup Y) = 31 - 7 \][/tex]
[tex]\[ n(X \cup Y) = 24 \][/tex]
Thus, the number of elements in the union of sets \( X \) and \( Y \) is:
[tex]\[ n(X \cup Y) = 24 \][/tex]
So, the correct answer is:
(B) 24
[tex]\[ n(X \cup Y) = n(X) + n(Y) - n(X \cap Y) \][/tex]
Here, \( n(X) \) represents the number of elements in set \( X \), \( n(Y) \) represents the number of elements in set \( Y \), and \( n(X \cap Y) \) represents the number of elements that are common to both sets \( X \) and \( Y \).
Given the values:
- \( n(X) = 12 \)
- \( n(Y) = 19 \)
- \( n(X \cap Y) = 7 \)
We substitute these values into the formula:
[tex]\[ n(X \cup Y) = 12 + 19 - 7 \][/tex]
Perform the arithmetic operations:
[tex]\[ n(X \cup Y) = 31 - 7 \][/tex]
[tex]\[ n(X \cup Y) = 24 \][/tex]
Thus, the number of elements in the union of sets \( X \) and \( Y \) is:
[tex]\[ n(X \cup Y) = 24 \][/tex]
So, the correct answer is:
(B) 24
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.