Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/04%3A_Sets/4.03%3A_Unions_and_IntersectionsWe can form a new set from existing sets by carrying out a set operation.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/02%3A_Logical_Reasoning/2.02%3A_Logically_Equivalent_StatementsTwo expressions are logically equivalent provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions. In this case, we...Two expressions are logically equivalent provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions. In this case, we write X≡Y and say that X and Y are logically equivalent.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/02%3A_Logical_Reasoning/2.02%3A_Logically_Equivalent_StatementsTwo expressions are logically equivalent provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions. In this case, we...Two expressions are logically equivalent provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions. In this case, we write X≡Y and say that X and Y are logically equivalent.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/05%3A_Set_Theory/5.03%3A_Properties_of_Set_OperationsThis section contains many results concerning the properties of the set operations. We have already proved some of the results. Others will be proved in this section or in the exercises. The primary p...This section contains many results concerning the properties of the set operations. We have already proved some of the results. Others will be proved in this section or in the exercises. The primary purpose of this section is to have in one place many of the properties of set operations that we may use in later proofs. These results are part of what is known as the algebra of sets or as set theory.
- https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Reasoning/2%3A_Basic_Concepts_of_Sets/2.5%3A_Properties_of_SetsThe following set properties are given here in preparation for the properties for addition and multiplication in arithmetic. Note the close similarity between these properties and their corresponding ...The following set properties are given here in preparation for the properties for addition and multiplication in arithmetic. Note the close similarity between these properties and their corresponding properties for addition and multiplication.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/4%3A_Sets/4.3%3A_Unions_and_IntersectionsDistributive laws: \(\begin{array}[t]{l} A \cup (B \cap C) = (A \cup B) \cap (A \cup C), \\ A \cap (B \cup C) = (A \cap B) \cup (A \cap C). \end{array}\) We need to show that \[A \cup (B \cap C) \subs...Distributive laws: \(\begin{array}[t]{l} A \cup (B \cap C) = (A \cup B) \cap (A \cup C), \\ A \cap (B \cup C) = (A \cap B) \cup (A \cap C). \end{array}\) We need to show that \[A \cup (B \cap C) \subseteq (A \cup B) \cap (A \cup C), \qquad\mbox{and}\qquad (A \cup B) \cap (A \cup C) \subseteq A \cup (B \cap C).\]
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/05%3A_Set_Theory/5.03%3A_Properties_of_Set_OperationsThis section contains many results concerning the properties of the set operations. We have already proved some of the results. Others will be proved in this section or in the exercises. The primary p...This section contains many results concerning the properties of the set operations. We have already proved some of the results. Others will be proved in this section or in the exercises. The primary purpose of this section is to have in one place many of the properties of set operations that we may use in later proofs. These results are part of what is known as the algebra of sets or as set theory.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/05%3A_Set_Theory/5.05%3A_Indexed_Families_of_SetsIn a similar manner, if \(\Lambda\) is a nonempty indexing set and \(\mathcal{A} = \{A_{\alpha}\ |\ \alpha \in \Lambda\}\) is an indexed family of sets, we can say that this indexed family of sets is ...In a similar manner, if \(\Lambda\) is a nonempty indexing set and \(\mathcal{A} = \{A_{\alpha}\ |\ \alpha \in \Lambda\}\) is an indexed family of sets, we can say that this indexed family of sets is disjoint provided that \(\bigcap_{\alpha \in \Lambda}^{} A_{\alpha} = \emptyset\).
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/05%3A_Set_Theory/5.05%3A_Indexed_Families_of_SetsIn a similar manner, if \(\Lambda\) is a nonempty indexing set and \(\mathcal{A} = \{A_{\alpha}\ |\ \alpha \in \Lambda\}\) is an indexed family of sets, we can say that this indexed family of sets is ...In a similar manner, if \(\Lambda\) is a nonempty indexing set and \(\mathcal{A} = \{A_{\alpha}\ |\ \alpha \in \Lambda\}\) is an indexed family of sets, we can say that this indexed family of sets is disjoint provided that \(\bigcap_{\alpha \in \Lambda}^{} A_{\alpha} = \emptyset\).
