Union and Intersection (Algebra 2) Flashcards

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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.

{1, 3, 10} Signup and view all the answers

If A = {1, 3, 7, 9, 10} and D = all even numbers between 1 and 11, find AUD.

{1, 2, 3, 4, 6, 7, 8, 9, 10} Signup and view all the answers

If A = {1, 3, 7, 9, 10} and D = all even numbers between 1 and 11, find A∩D.

{10} Signup and view all the answers

If A={1, 3, 7, 9, 10} and E={0}, find AUE.

{0, 1, 3, 7, 9, 10} Signup and view all the answers

If A={1, 3, 7, 9, 10} and E={0}, find A∩E.

the empty set Signup and view all the answers

If B = {2, 5, 7, 8, 9, 10} and C = {0, 1, 3, 10}, find BUC.

{0, 1, 2, 3, 5, 7, 8, 9, 10} Signup and view all the answers

If B = {2, 5, 7, 8, 9, 10} and C = {0, 1, 3, 10}, find B∩C.

{10} Signup and view all the answers

If B = {2, 5, 7, 8, 9, 10} and D = all even numbers between 1 and 11, find BUD.

{2, 4, 5, 6, 7, 8, 9, 10} Signup and view all the answers

If B = {2, 5, 7, 8, 9, 10} and D = all even numbers between 1 and 11, find B∩D.

{2, 8, 10} Signup and view all the answers

If B = {2, 5, 7, 8, 9, 10} and E = {0}, find BUE.

{0, 2, 5, 7, 8, 9, 10} Signup and view all the answers

If B = {2, 5, 7, 8, 9, 10} and E = {0}, find B∩E.

the empty set Signup and view all the answers

If C = {0, 1, 3, 10} and D = all even numbers between 1 and 11, find CUD.

{0, 1, 2, 3, 4, 6, 8, 10} Signup and view all the answers

If C = {0, 1, 3, 10} and D = all even numbers between 1 and 11, find C∩D.

{10} Signup and view all the answers

If C = {0, 1, 3, 10} and E = {0}, find CUE.

{0, 1, 3, 10} Signup and view all the answers

If C = {0, 1, 3, 10} and E = {0}, find C∩E.

{0} Signup and view all the answers

If D = all even numbers between 1 and 11, and E = {0}, find DUE.

{0, 2, 4, 6, 8, 10} Signup and view all the answers

If D = all even numbers between 1 and 11, and E = {0}, find D∩E.

the empty set Signup and view all the answers

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

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}.
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

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}.
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

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}.
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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Test your understanding of set operations with our Algebra 2 flashcards focusing on union and intersection. Each card provides examples to help you grasp the concepts of combining and comparing sets. Perfect for review or quick study sessions.