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Questions and Answers
What is the formula for the union of two sets A and B?
What is the formula for the union of two sets A and B?
- A ∪ B = {x | x ∉ A and x ∉ B}
- A ∪ B = {x | x ∈ A or x ∈ B} (correct)
- A ∪ B = {x | x ∈ A and x ∈ B}
- A ∪ B = {x | x ∈ A - x ∈ B}
What is the intersection of sets A = {1, 2, 3} and B = {3, 4, 5}?
What is the intersection of sets A = {1, 2, 3} and B = {3, 4, 5}?
- {1, 2}
- {3} (correct)
- {4, 5}
- {1, 2, 3, 4, 5}
What is the difference of sets A = {1, 2, 3} and B = {3, 4, 5}?
What is the difference of sets A = {1, 2, 3} and B = {3, 4, 5}?
- {3}
- {1, 2, 3, 4, 5}
- {4, 5}
- {1, 2} (correct)
Is the difference of sets A and B commutative?
Is the difference of sets A and B commutative?
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What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?
What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?
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Study Notes
Sets
Union Of Sets
- The union of two sets A and B, denoted as A ∪ B, is the set of all elements that are in A, in B, or in both.
- Formula: A ∪ B = {x | x ∈ A or x ∈ B}
- Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}
Intersection Of Sets
- The intersection of two sets A and B, denoted as A ∩ B, is the set of all elements that are common to both A and B.
- Formula: A ∩ B = {x | x ∈ A and x ∈ B}
- Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}
Difference Of Sets
- The difference of two sets A and B, denoted as A \ B, is the set of all elements that are in A but not in B.
- Formula: A \ B = {x | x ∈ A and x ∉ B}
- Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A \ B = {1, 2}
- Note: The difference of sets is not commutative, i.e. A \ B ≠B \ A in general.
Sets
Union of Sets
- Union of two sets A and B, denoted as A ∪ B, contains all elements from A, B, or both.
- Formula: A ∪ B = {x | x ∈ A or x ∈ B}
- Example: A = {1, 2, 3} and B = {3, 4, 5} → A ∪ B = {1, 2, 3, 4, 5}
Intersection of Sets
- Intersection of two sets A and B, denoted as A ∩ B, contains all elements common to both A and B.
- Formula: A ∩ B = {x | x ∈ A and x ∈ B}
- Example: A = {1, 2, 3} and B = {3, 4, 5} → A ∩ B = {3}
Difference of Sets
- Difference of two sets A and B, denoted as A \ B, contains all elements in A but not in B.
- Formula: A \ B = {x | x ∈ A and x ∉ B}
- Example: A = {1, 2, 3} and B = {3, 4, 5} → A \ B = {1, 2}
- Note: A \ B ≠B \ A in general, as the difference of sets is not commutative.
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