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Questions and Answers
Given the universal set $U = {1, 2, 3, 4, 5, 6, 7}$ and set $A = {2, 4, 6}$, what is the complement of A (A')?
Given the universal set $U = {1, 2, 3, 4, 5, 6, 7}$ and set $A = {2, 4, 6}$, what is the complement of A (A')?
- $\emptyset$
- $\left\{1, 2, 3, 4, 5, 6, 7\right\}$
- $\left\{2, 4, 6\right\}$
- $\left\{1, 3, 5, 7\right\}$ (correct)
If $A = {a, b, c, d}$ and $B = {c, d, e, f}$, what is A - B?
If $A = {a, b, c, d}$ and $B = {c, d, e, f}$, what is A - B?
- $\left\{e, f\right\}$
- $\left\{a, b\right\}$ (correct)
- $\left\{a, b, c, d, e, f\right\}$
- $\left\{c, d\right\}$
Which of the following is equivalent to A - B?
Which of the following is equivalent to A - B?
- B - A
- A' ∪ B
- A ∩ B' (correct)
- A ∪ B
Given $A = {1, 2, 3, 4}$ and $B = {3, 4, 5, 6}$, what is the intersection of A and B (A ∩ B)?
Given $A = {1, 2, 3, 4}$ and $B = {3, 4, 5, 6}$, what is the intersection of A and B (A ∩ B)?
If sets A and B are disjoint, what is their intersection (A ∩ B)?
If sets A and B are disjoint, what is their intersection (A ∩ B)?
Which of the following statements is always true for any set A?
Which of the following statements is always true for any set A?
Given $A = {2, 4, 6}$ and $B = {1, 3, 5}$, what is the union of A and B (A ∪ B)?
Given $A = {2, 4, 6}$ and $B = {1, 3, 5}$, what is the union of A and B (A ∪ B)?
Which of the following statements is always true?
Which of the following statements is always true?
If $A = {1, 2}$, $B = {2, 3}$, and $C = {3, 4}$, what is A ∪ (B ∩ C)?
If $A = {1, 2}$, $B = {2, 3}$, and $C = {3, 4}$, what is A ∪ (B ∩ C)?
Given the universal set $U = {1, 2, 3, 4, 5}$ and $A = {1, 2}$, $B = {2, 3}$. Determine (A ∪ B)'.
Given the universal set $U = {1, 2, 3, 4, 5}$ and $A = {1, 2}$, $B = {2, 3}$. Determine (A ∪ B)'.
Flashcards
Complement of a Set A
Complement of a Set A
Elements in the universal set U that are not in A.
Difference of Sets A and B (A - B)
Difference of Sets A and B (A - B)
Elements in A but not in B.
Intersection of Sets A and B (A ∩ B)
Intersection of Sets A and B (A ∩ B)
Elements common to both A and B.
Disjoint Sets
Disjoint Sets
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Union of Sets A and B (A ∪ B)
Union of Sets A and B (A ∪ B)
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Commutative Property of Intersection
Commutative Property of Intersection
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Associative Property of Intersection
Associative Property of Intersection
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Intersection with the Empty Set
Intersection with the Empty Set
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Intersection with the Universal Set
Intersection with the Universal Set
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Commutative Property of Union
Commutative Property of Union
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Study Notes
- Set operations combine sets to form new sets, altering or comparing them.
Complement
- The complement of a set A (denoted A' or Aᶜ) contains all elements in the universal set U that are not in A.
- If U = {1, 2, 3, 4, 5} and A = {1, 3}, then A' = {2, 4, 5}.
- The complement depends on the universal set; changing U changes the complement of A.
Difference
- The difference of two sets A and B (denoted A - B or A \ B) contains elements that are in A but not in B.
- If A = {1, 2, 3} and B = {2, 4}, then A - B = {1, 3}.
- The difference A - B is not the same as B - A unless A and B are identical. For the previous example, B - A = {4}.
- A - B can also be expressed as A ∩ B', the intersection of A and the complement of B.
- If A is a subset of B, then A - B is the empty set, denoted as ∅ or {}.
Intersection
- The intersection of two sets A and B (denoted A ∩ B) contains all elements that are common to both A and B.
- If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.
- If A and B have no elements in common, their intersection is the empty set (A ∩ B = ∅), and A and B are called disjoint sets.
- The intersection operation is commutative: A ∩ B = B ∩ A.
- The intersection operation is associative: (A ∩ B) ∩ C = A ∩ (B ∩ C).
- The intersection of a set with the empty set is the empty set: A ∩ ∅ = ∅.
- The intersection of a set with the universal set is the set itself: A ∩ U = A.
- The intersection operation is idempotent: A ∩ A = A.
- The intersection distributes over the union: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
Union
- The union of two sets A and B (denoted A ∪ B) contains all elements that are in A, or in B, or in both.
- If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.
- The union operation is commutative: A ∪ B = B ∪ A.
- The union operation is associative: (A ∪ B) ∪ C = A ∪ (B ∪ C).
- The union of a set with the empty set is the set itself: A ∪ ∅ = A.
- The union of a set with the universal set is the universal set: A ∪ U = U.
- The union operation is idempotent: A ∪ A = A.
- The union distributes over the intersection: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
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