Math worksheet on intersection and union of sets with problems and instructions.

Let's solve each problem step by step.

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Definitions:

- Intersection (A ∩ B): Elements that are in both sets A and B.
- Union (A ∪ B): All elements that are in either set A or B (or both), with no duplicates.

We will list the answers using curly braces `{}` and separate elements with commas, without spaces.

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1. A = {1,2,3,4,5,6,7,8} and B = {1,2,3,5,7,11}

(a) A ∩ B
Common elements: 1, 2, 3, 5, 7
→ `{1,2,3,5,7}`

(b) A ∪ B
All elements from both sets: 1,2,3,4,5,6,7,8,11
→ `{1,2,3,4,5,6,7,8,11}`

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2. A = {4,5,6,7,10} and B = {5,7,11}

(a) A ∩ B
Common elements: 5, 7
→ `{5,7}`

(b) A ∪ B
All elements: 4,5,6,7,10,11
→ `{4,5,6,7,10,11}`

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3. A = {4,6,8,10,12} and B = {3,6,9,12}

(a) A ∩ B
Common elements: 6, 12
→ `{6,12}`

(b) A ∪ B
All elements: 3,4,6,8,9,10,12
→ `{3,4,6,8,9,10,12}`

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4. A = {0,2,4,6} and B = {1,3,5}

(a) A ∩ B
No common elements → empty set
→ `{}`

(b) A ∪ B
All elements: 0,1,2,3,4,5,6
→ `{0,1,2,3,4,5,6}`

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5. A = {-3,-2,-1,0} and B = {0,2,3,4}

(a) A ∩ B
Common element: 0
→ `{0}`

(b) A ∪ B
All elements: -3,-2,-1,0,2,3,4
→ `{-3,-2,-1,0,2,3,4}`

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6. A = {0,1,2,3,4,5} and B = {6,7,8,9,10}

(a) A ∩ B
No common elements → empty set
→ `{}`

(b) A ∪ B
All elements: 0,1,2,3,4,5,6,7,8,9,10
→ `{0,1,2,3,4,5,6,7,8,9,10}`

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✔ Final Answers:

1.
(a) `{1,2,3,5,7}`
(b) `{1,2,3,4,5,6,7,8,11}`

2.
(a) `{5,7}`
(b) `{4,5,6,7,10,11}`

3.
(a) `{6,12}`
(b) `{3,4,6,8,9,10,12}`

4.
(a) `{}`
(b) `{0,1,2,3,4,5,6}`

5.
(a) `{0}`
(b) `{-3,-2,-1,0,2,3,4}`

6.
(a) `{}`
(b) `{0,1,2,3,4,5,6,7,8,9,10}`

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