Worksheet 1 - Intersection and Union of Sets

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}
B = {1,2,3,5,7,11}

(a) A ∩ B: Elements common to both A and B
→ 1, 2, 3, 5, 7
→ {1,2,3,5,7}

(b) A ∪ B: All elements from both sets (no duplicates)
→ 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}
B = {5,7,11}

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

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

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3.

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

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

(b) A ∪ B: All unique 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}
B = {1,3,5}

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

(b) A ∪ B: All unique 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}
B = {0,2,3,4}

(a) A ∩ B: Common elements
→ 0
→ {0}

(b) A ∪ B: All unique 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}
B = {6,7,8,9,10}

(a) A ∩ B: Common elements
→ None
→ {}

(b) A ∪ B: All unique 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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