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4.1.4: Cardinality
https://math.libretexts.org/Courses/American_River_College/Math_300%3A_My_Math_Ideas_Textbook_(Kinoshita)/04%3A_Sets/4.01%3A_Sets/4.1.04%3A_Cardinality
Notice that while the cardinality of $F$ is $70 \%$ and the cardinality of $T$ is $40 \%$ , the cardinality of $F \cup T$ is not simply $70 \%+40 \%$ , since that would count those who use b...Notice that while the cardinality of $F$ is $70 \%$ and the cardinality of $T$ is $40 \%$ , the cardinality of $F \cup T$ is not simply $70 \%+40 \%$ , since that would count those who use both services twice. To find the cardinality of $F \cup T$ , we can add the cardinality of $F$ and the cardinality of $T$ , then subtract those in intersection that we've counted twice.
7.4: Cardinality
https://math.libretexts.org/Courses/Highline_College/Math_111%3A_College_Algebra/07%3A_Sets/7.04%3A_Cardinality
Notice that while the cardinality of $F$ is $70 \%$ and the cardinality of $T$ is $40 \%$ , the cardinality of $F \cup T$ is not simply $70 \%+40 \%$ , since that would count those who use b...Notice that while the cardinality of $F$ is $70 \%$ and the cardinality of $T$ is $40 \%$ , the cardinality of $F \cup T$ is not simply $70 \%+40 \%$ , since that would count those who use both services twice. To find the cardinality of $F \cup T$ , we can add the cardinality of $F$ and the cardinality of $T$ , then subtract those in intersection that we've counted twice.
8.5: The Continuum Hypothesis and The Generalized Continuum Hypothesis
https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/08%3A_Cardinality/8.05%3A_The_Continuum_Hypothesis_and_The_Generalized_Continuum_Hypothesis
The word “continuum” in the title of this section is used to indicate sets of points that have a certain continuity property. For example, in a real interval it is possible to move from one point to a...The word “continuum” in the title of this section is used to indicate sets of points that have a certain continuity property. For example, in a real interval it is possible to move from one point to another, in a smooth fashion, without ever leaving the interval. In a range of rational numbers this is not possible, because there are irrational values in between every pair of rationals.
7.4: Cardinality
https://math.libretexts.org/Workbench/Business_Precalculus/07%3A_Sets/7.04%3A_Cardinality
Notice that while the cardinality of $F$ is $70 \%$ and the cardinality of $T$ is $40 \%$ , the cardinality of $F \cup T$ is not simply $70 \%+40 \%$ , since that would count those who use b...Notice that while the cardinality of $F$ is $70 \%$ and the cardinality of $T$ is $40 \%$ , the cardinality of $F \cup T$ is not simply $70 \%+40 \%$ , since that would count those who use both services twice. To find the cardinality of $F \cup T$ , we can add the cardinality of $F$ and the cardinality of $T$ , then subtract those in intersection that we've counted twice.
1.3: Applications of Sets
https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1130_Mathematical_Ideas_Mirtova_Jones_(PGCC%3A_Fall_2022)/01%3A_Sets/1.03%3A_Applications_of_Sets
We can also see that those who drink neither are those not contained in the any of the three other groupings, so we can count those by subtracting from the cardinality of the universal set, 200: \(\be...We can also see that those who drink neither are those not contained in the any of the three other groupings, so we can count those by subtracting from the cardinality of the universal set, 200: $\begin{array}{ll} \text{43 believed in UFOs} & \text{44 believed in ghosts} \\ \text{25 believed in Bigfoot} & \text{10 believed in UFOs and ghosts} \\ \text{8 believed in ghosts and Bigfoot} & \text{5 believed in UFOs and Bigfoot} \\ \text{2 believed in all three} & \text{} \end{array}$
5.1: Sets and Operations on Sets
https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/05%3A_Set_Theory/5.01%3A_Sets_and_Operations_on_Sets
We have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have ...We have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have already been defined. In fact, we will form these new sets using the logical operators of conjunction (and), disjunction (or), and negation (not).
5.1: Sets and Operations on Sets
https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/05%3A_Set_Theory/5.01%3A_Sets_and_Operations_on_Sets
We have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have ...We have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have already been defined. In fact, we will form these new sets using the logical operators of conjunction (and), disjunction (or), and negation (not).
2.1: Subsets and Equality
https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Reasoning/2%3A_Basic_Concepts_of_Sets/2.1%3A_Subsets_and_Equality
Sets can be arranged into smaller groups called subsets. Sets can also be equal to, each other.
9.2: How Big is Infinity? Or Is it “Infinities”?
https://math.libretexts.org/Courses/Coastline_College/Math_C100%3A_Liberal_Arts_Mathematics_(Tran)/09%3A_Selected_Topics/9.02%3A_How_Big_is_Infinity_Or_Is_it_Infinities
There are infinitely many levels of infinities.
9.1: Finite Sets
https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/09%3A_Finite_and_Infinite_Sets/9.01%3A_Finite_Sets
If $A$ is a finite set and $x \notin A$ , then $A \cup \{x\}$ is a finite set and $\text{card}(A \cup \{x\}) = \text{card}(A) + 1$ . If $S$ is a finite set and $A$ is a subset of $S$ , then...If $A$ is a finite set and $x \notin A$ , then $A \cup \{x\}$ is a finite set and $\text{card}(A \cup \{x\}) = \text{card}(A) + 1$ . If $S$ is a finite set and $A$ is a subset of $S$ , then $A$ is a finite set and $\text{card}(A) \le \text{card}(S)$ . If $A$ is a finite set and $x \in A$ , then $A - \{x\}$ is a finite set and $\text{card}(A - \{x\}) = \text{card} (A) - 1$
2.4: Survey Problems
https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/02%3A_Set_Theory/2.04%3A_Survey_Problems
\(\begin{array}{ll} \text{21 were taking a SS course} & \text{26 were taking a HM course} \\ \text{19 were taking a NS course} & \text{9 were taking SS and HM} \\ \text{7 were taking SS and NS} & \tex... $\begin{array}{ll} \text{21 were taking a SS course} & \text{26 were taking a HM course} \\ \text{19 were taking a NS course} & \text{9 were taking SS and HM} \\ \text{7 were taking SS and NS} & \text{10 were taking HM and NS} \\ \text{3 were taking all three} & \text{7 were taking none} \end{array}$

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