Use the following to answer the next question.
We have the following two sets below:
[tex]
\begin{array}{c}
A:\{\beta, \varphi, \pi, \theta, \mu, \kappa, \sigma\} \
B:\{\chi, \pi, \theta, \xi, \beta, \sigma, \lambda, \omega\}
\end{array}
[/tex]
The value of [tex]n(A \cup B)[/tex] is
A. 4
B. 7
C. 11
D. 15
Answer (2)
List elements of set A.
List elements of set B.
Combine elements of A and B, removing duplicates.
Count the unique elements in the union: n ( A c u pB ) = 11 .
The value of n ( A c u pB ) is 11 .
Explanation
Understanding the Problem We are given two sets, A and B, and we need to find the number of elements in their union, denoted as n ( A c u pB ) . The union of two sets contains all the unique elements present in either set.
Analyzing Set A Set A contains the elements: β , φ , π , θ , μ , κ , σ . So, n ( A ) = 7 .
Analyzing Set B Set B contains the elements: χ , π , θ , ξ , β , σ , λ , ω . So, n ( B ) = 8 .
Finding the Union of A and B To find A ∪ B , we combine the elements of A and B, removing any duplicates. The elements in A ∪ B are: β , φ , π , θ , μ , κ , σ , χ , ξ , λ , ω .
Counting Elements in the Union Now, we count the number of unique elements in A ∪ B . There are 11 unique elements. Therefore, n ( A ∪ B ) = 11 .
Final Answer The value of n ( A ∪ B ) is 11.
Examples
Understanding sets and their unions is crucial in many areas, such as database management, where you might want to combine customer lists from different sources, ensuring you don't have duplicate entries. In probability, when calculating the likelihood of either event A or event B occurring, you need to consider the union of the events. For example, if event A is 'drawing a heart from a deck of cards' and event B is 'drawing a king,' the union helps you find the probability of drawing a heart or a king.
The value of n ( A ∪ B ) is calculated by finding the union of sets A and B and counting the unique elements. The combined unique elements result in a total of 11. Therefore, the answer is option C: 11.
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