Questions and Answers
If A = {1, 3, 7, 9, 10} and B = {2, 5, 7, 8, 9, 10}, find AUB.
{1, 2, 3, 5, 7, 8, 9, 10}
If A = {1, 3, 7, 9, 10} and B = {2, 5, 7, 8, 9, 10}, find A∩B.
{7, 9, 10}
If A = {1, 3, 7, 9, 10} and C = {0, 1, 3, 10}, find AUC.
{0, 1, 3, 7, 9, 10}
If A = {1, 3, 7, 9, 10} and C = {0, 1, 3, 10}, find A∩C.
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If A = {1, 3, 7, 9, 10} and D = all even numbers between 1 and 11, find AUD.
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If A = {1, 3, 7, 9, 10} and D = all even numbers between 1 and 11, find A∩D.
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If A={1, 3, 7, 9, 10} and E={0}, find AUE.
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If A={1, 3, 7, 9, 10} and E={0}, find A∩E.
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If B = {2, 5, 7, 8, 9, 10} and C = {0, 1, 3, 10}, find BUC.
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If B = {2, 5, 7, 8, 9, 10} and C = {0, 1, 3, 10}, find B∩C.
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If B = {2, 5, 7, 8, 9, 10} and D = all even numbers between 1 and 11, find BUD.
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If B = {2, 5, 7, 8, 9, 10} and D = all even numbers between 1 and 11, find B∩D.
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If B = {2, 5, 7, 8, 9, 10} and E = {0}, find BUE.
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If B = {2, 5, 7, 8, 9, 10} and E = {0}, find B∩E.
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If C = {0, 1, 3, 10} and D = all even numbers between 1 and 11, find CUD.
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If C = {0, 1, 3, 10} and D = all even numbers between 1 and 11, find C∩D.
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If C = {0, 1, 3, 10} and E = {0}, find CUE.
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If C = {0, 1, 3, 10} and E = {0}, find C∩E.
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If D = all even numbers between 1 and 11, and E = {0}, find DUE.
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If D = all even numbers between 1 and 11, and E = {0}, find D∩E.
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Study Notes
Union and Intersection Basics
- Union (A ∪ B): Includes all elements from both sets, combining duplicates.
- Intersection (A ∩ B): Includes only the elements common to both sets.
Key Examples of Unions and Intersections
- For sets A = {1, 3, 7, 9, 10} and B = {2, 5, 7, 8, 9, 10},
- Union A ∪ B results in {1, 2, 3, 5, 7, 8, 9, 10}.
- Intersection A ∩ B gives {7, 9, 10}.
Additional Set Operations
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For sets A = {1, 3, 7, 9, 10} and C = {0, 1, 3, 10},
- Union A ∪ C is {0, 1, 3, 7, 9, 10}.
- Intersection A ∩ C yields {1, 3, 10}.
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For A and D (the even numbers {2, 4, 6, 8, 10}),
- A ∪ D becomes {1, 2, 3, 4, 6, 7, 8, 9, 10}.
- A ∩ D results in {10}.
Exploring Empty Sets and Unique Elements
- For A = {1, 3, 7, 9, 10} and E = {0},
- A ∪ E is {0, 1, 3, 7, 9, 10}.
- Intersection A ∩ E is the empty set, indicating no shared elements.
Operations with Set B
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For B = {2, 5, 7, 8, 9, 10} and C = {0, 1, 3, 10},
- Union B ∪ C results in {0, 1, 2, 3, 5, 7, 8, 9, 10}.
- Intersection B ∩ C gives {10}.
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For B and D,
- B ∪ D, where D includes even numbers, results in {2, 4, 5, 6, 7, 8, 9, 10}.
- B ∩ D is {2, 8, 10}.
Operations with Set C
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For C = {0, 1, 3, 10} and D (even numbers),
- Union C ∪ D is {0, 1, 2, 3, 4, 6, 8, 10}.
- Intersection C ∩ D results in {10}.
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With C and E = {0},
- C ∪ E stays {0, 1, 3, 10}, indicating no change.
- Intersection C ∩ E gives {0}.
Union and Intersection with Set D and E
- D contains even numbers, and combining with E = {0} gives:
- Union D ∪ E results in {0, 2, 4, 6, 8, 10}.
- Intersection D ∩ E is empty, confirming no overlap with odd numbers.
These operations illustrate foundational concepts in set theory, aiding in understanding relationships and cardinalities among various sets.
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