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ACTIVITY 6.3: SPIN THE WHEEL
A spinning wheel is divided into 12 equal sectors and
numbered 1-12. Make a Venn diagram illustrating the events
listed. Then answer the following.
U =
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = getting an odd number
B
=
getting an even number
C = getting a prime number
1. What is AUB?
2. What is AU C?
3. What is BUC?
4. What is AB?
5. What is An C?
6. What is B OC?
0

Sagot :

Answer:

Let's start by defining the sets:

- \( U \) (Universal set) = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}

- \( A \) (Odd numbers) = \{1, 3, 5, 7, 9, 11\}

- \( B \) (Even numbers) = \{2, 4, 6, 8, 10, 12\}

- \( C \) (Prime numbers) = \{2, 3, 5, 7, 11\}

Now, let's create the Venn diagram and answer the questions:

1. **\( A \cup B \) (A union B)**: This set includes all elements that are in \( A \) or \( B \) or both.

- \( A \cup B \) = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}

- Since every number in the universal set is either odd or even, \( A \cup B = U \).

2. **\( A \cup C \) (A union C)**: This set includes all elements that are in \( A \) or \( C \) or both.

- \( A \cup C \) = \{1, 3, 5, 7, 9, 11, 2\}

3. **\( B \cup C \) (B union C)**: This set includes all elements that are in \( B \) or \( C \) or both.

- \( B \cup C \) = \{2, 4, 6, 8, 10, 12, 3, 5, 7, 11\}

4. **\( A \cap B \) (A intersection B)**: This set includes all elements that are in both \( A \) and \( B \).

- \( A \cap B \) = \{\} (There are no numbers that are both odd and even)

5. **\( A \cap C \) (A intersection C)**: This set includes all elements that are in both \( A \) and \( C \).

- \( A \cap C \) = \{3, 5, 7, 11\}

6. **\( B \cap C \) (B intersection C)**: This set includes all elements that are in both \( B \) and \( C \).

- \( B \cap C \) = \{2\}

Here's the Venn diagram:

```

_______A_______

/ \

/ {1,3,5,7,9,11} \

/ \

/ \

/ _______C_______ \

/ / {2,3,5,7,11} \ \

/ / \ \

/ / \ \

/ / B \ \

/ / {2,4,6,8,10,12} \ \

/ /__________________________\ \

/______________________________________\

```

From the Venn diagram, you can clearly see the sets and their intersections.

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