Question

Math

Posted 6 months ago

```
Given the following Venn diagram, find $n\left[\left(\mathrm{C}^{\mathrm{c}} \cup \mathrm{B}^{\mathrm{c}}\right)^{c}\right]$.
58
54
20
17
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

Identify the sets and their elements from the Venn diagram. Set A: {11, 15, 10, 9}, Set B: {15, 5, 9, 11}, Set C: {10, 9, 11, 12}

step 2

Determine the elements in the complement of set C, $C^c$. Since the universal set U is not fully specified, we assume it includes all elements mentioned: {5, 9, 10, 11, 12, 15}. Thus, $C^c$ = {5, 15}

step 3

Determine the elements in the complement of set B, $B^c$. Using the same universal set, $B^c$ = {10, 12}

step 4

Find the union of the complements, $C^c \cup B^c$. This results in the set {5, 10, 12, 15}

step 5

Find the complement of the union, $(C^c \cup B^c)^c$. This includes all elements in the universal set U that are not in {5, 10, 12, 15}. Thus, $(C^c \cup B^c)^c$ = {9, 11}

step 6

Count the number of elements in $(C^c \cup B^c)^c$. There are 2 elements: 9 and 11. Therefore, $n[(C^c \cup B^c)^c] = 2$

Answer

2

Key Concept

Set Operations and Complements

Explanation

The problem involves finding the complement of the union of the complements of two sets within a universal set. This requires understanding and applying set operations and complements.

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