Sets exercise - Free Printable

Let's solve each question step by step using the Venn diagram and the information provided.

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Given:

- The universal set $ U $ = {set of counting numbers to twenty}
→ So, $ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\} $

- The Venn diagram shows:
- Set A and Set B overlapping.
- Numbers in the regions:
- Only in A: 4, 12
- Only in B: 9, 18
- In both A and B (intersection): 1, 2, 3, 6

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Question 1: What are the members of the universal set?

The universal set is defined as the set of counting numbers from 1 to 20.

✔ Answer:
$$
\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}
$$

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Question 2: What are the members of set A?

Set A includes:
- Elements only in A: 4, 12
- Elements in both A and B: 1, 2, 3, 6

So, combine them:

✔ Answer:
$$
\{1, 2, 3, 4, 6, 12\}
$$

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Question 3: What are the members of set B?

Set B includes:
- Elements only in B: 9, 18
- Elements in both A and B: 1, 2, 3, 6

So, combine them:

✔ Answer:
$$
\{1, 2, 3, 6, 9, 18\}
$$

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Question 4: List the members that intersect.

The intersection $ A \cap B $ is the region where the two circles overlap.

From the diagram: 1, 2, 3, 6

✔ Answer:
$$
\{1, 2, 3, 6\}
$$

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Question 5: What members are in the universal set but not a member of Set A nor Set B?

We need to find elements in $ U $ that are not in A or B.

First, list all elements in A ∪ B (union of A and B):

- From A: 1, 2, 3, 4, 6, 12
- From B: 9, 18
- Combined: $ A \cup B = \{1, 2, 3, 4, 6, 9, 12, 18\} $

Now, subtract these from the universal set $ U $:

$ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\} $

Remove $ \{1, 2, 3, 4, 6, 9, 12, 18\} $

Remaining elements:

$$
\{5, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20\}
$$

✔ Answer:
$$
\{5, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20\}
$$

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✔ Final Answers:

1. Universal set: $ \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\} $

2. Set A: $ \{1, 2, 3, 4, 6, 12\} $

3. Set B: $ \{1, 2, 3, 6, 9, 18\} $

4. Intersection (A ∩ B): $ \{1, 2, 3, 6\} $

5. Not in A or B: $ \{5, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20\} $

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