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Questions and Answers
Which one of the following symbols represents the union of sets?
Which one of the following symbols represents the union of sets?
- $\subseteq$
- $\setminus$
- $\cap$
- $\cup$ (correct)
Which one of the following symbols represents the intersection of sets?
Which one of the following symbols represents the intersection of sets?
- $\setminus$
- $\cup$
- $\cap$ (correct)
- $\subseteq$
Which one of the following symbols represents the difference of sets?
Which one of the following symbols represents the difference of sets?
- $\subseteq$
- $\setminus$ (correct)
- $\cup$
- $\cap$
Which one of the following symbols represents a subset relationship between sets?
Which one of the following symbols represents a subset relationship between sets?
Which one of the following symbols represents a superset relationship between sets?
Which one of the following symbols represents a superset relationship between sets?
Set $A$ contains the elements {1, 2}, and set $B$ contains the elements {2, 3}. The union of sets $A$ and $B$ is equal to
Set $A$ contains the elements {1, 2}, and set $B$ contains the elements {2, 3}. The union of sets $A$ and $B$ is equal to
If sets $A_1$, $A_2$, and $A_3$ are defined as $A_1={a,b,c}$, $A_2={c,h}$, $A_3={a,d}$, then the union of sets $A_1$, $A_2$, and $A_3$ is equal to
If sets $A_1$, $A_2$, and $A_3$ are defined as $A_1={a,b,c}$, $A_2={c,h}$, $A_3={a,d}$, then the union of sets $A_1$, $A_2$, and $A_3$ is equal to
The union of sets $A$ and $B$ is shown by the shaded area in the Venn diagram. If the union of sets $A$ and $B$ is equal to set $B$ union set $A$, then it follows that
The union of sets $A$ and $B$ is shown by the shaded area in the Venn diagram. If the union of sets $A$ and $B$ is equal to set $B$ union set $A$, then it follows that
The complement of set $A$ is defined as the set of elements that are not in set $A$. If the complement of set $A$ is denoted as $A'$, then the expression $(x \in A')$ is equivalent to
The complement of set $A$ is defined as the set of elements that are not in set $A$. If the complement of set $A$ is denoted as $A'$, then the expression $(x \in A')$ is equivalent to
The union of three or more sets can be defined using the symbol $\bigcup$. For example, if $A_1$, $A_2$, $A_3$ are $n$ sets, their union $A_1 \cup A_2 \cup A_3 \cdots \cup A_n$ can be written more compactly as
The union of three or more sets can be defined using the symbol $\bigcup$. For example, if $A_1$, $A_2$, $A_3$ are $n$ sets, their union $A_1 \cup A_2 \cup A_3 \cdots \cup A_n$ can be written more compactly as
Flashcards
Union of sets symbol
Union of sets symbol
Represents the combination of elements from two or more sets.
Intersection of sets symbol
Intersection of sets symbol
Represents the elements that are common to two or more sets.
Difference of sets symbol
Difference of sets symbol
Represents elements in the first set but not in the second set.
Subset relationship symbol
Subset relationship symbol
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Union of A{1,2} and B{2,3}
Union of A{1,2} and B{2,3}
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Union of A₁{a,b,c}, A₂{c,h}, A₃{a,d}
Union of A₁{a,b,c}, A₂{c,h}, A₃{a,d}
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A ∪ B = B ∪ A
A ∪ B = B ∪ A
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x ∈ A' equivalent
x ∈ A' equivalent
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Compact Union Notation
Compact Union Notation
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Study Notes
Set Operations Overview
- A set operation combines elements from one or more sets to create a new set.
- Basic operations include union, intersection, complement, and difference.
Union of Sets
- The union of two sets (A) and (B) includes all elements in either set: (A \cup B).
- Example: ({1,2} \cup {2,3} = {1,2,3}).
- Membership condition: (x \in (A \cup B)) if (x \in A) or (x \in B).
- Union is commutative: (A \cup B = B \cup A).
- For multiple sets (A_1, A_2, A_3, \ldots, A_n), the union is expressed as (\bigcup_{i=1}^{n} A_i).
Intersection of Sets
- Intersection gives all elements common to both sets (A) and (B), noted as (A \cap B).
Complement of a Set
- The complement of a set (A) contains all elements not in (A).
Difference of Sets
- The difference (A - B) includes elements in (A) but not in (B).
Mutually Exclusive Sets
- Two sets are mutually exclusive if they have no elements in common: (A \cap B = \emptyset).
Partitions of a Set
- A partition divides a set into disjoint subsets that completely cover the original set.
De Morgan's Laws
- Relate intersection and union through complements:
- ((A \cup B)^c = A^c \cap B^c)
- ((A \cap B)^c = A^c \cup B^c)
Distributive Law
- Describes how union and intersection distribute over each other:
- (A \cap (B \cup C) = (A \cap B) \cup (A \cap C))
- (A \cup (B \cap C) = (A \cup B) \cap (A \cup C))
Cartesian Product
- The Cartesian product of sets (A) and (B), denoted (A \times B), consists of all ordered pairs ((a, b)) where (a \in A) and (b \in B).
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