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  • https://math.libretexts.org/Bookshelves/Applied_Mathematics/Understanding_Elementary_Mathematics_(Harland)/01%3A_Set_Theory
    The Manipulatives listed below are to be used with this workbook. You will be using the material cards to make your own manipulatives in order to do hands on activities in some of the exercise sets. Y...The Manipulatives listed below are to be used with this workbook. You will be using the material cards to make your own manipulatives in order to do hands on activities in some of the exercise sets. You should prepare them ahead of time, and keep each type of manipulative in its own baggie. The manipulatives to be used in an exercise set are listed at the beginning of that set. You should also have handy a calculator, scissors, tape, colored pencils, pens, markers, highlighters and/or crayons.
  • https://math.libretexts.org/Courses/Coastline_College/Math_C104%3A_Mathematics_for_Elementary_Teachers_(Tran)/02%3A_Set_Theory
    The Manipulatives listed below are to be used with this workbook. You will be using the material cards to make your own manipulatives in order to do hands on activities in some of the exercise sets. Y...The Manipulatives listed below are to be used with this workbook. You will be using the material cards to make your own manipulatives in order to do hands on activities in some of the exercise sets. You should prepare them ahead of time, and keep each type of manipulative in its own baggie. The manipulatives to be used in an exercise set are listed at the beginning of that set. You should also have handy a calculator, scissors, tape, colored pencils, pens, markers, highlighters and/or crayons.
  • https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/05%3A_Set_Theory
    Thumbnail: A Venn diagram illustrating the intersection of two sets. (Public Domain; Cepheus).
  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/06%3A_Appendix/6.02%3A_B-_Glossary
    This page outlines shorthand notation for number sets in functions, defining \(Z\) as integers and \(R\) as real numbers. It specifies \(Z^+\) for positive integers (counting numbers) and \(Z^+ \cup \...This page outlines shorthand notation for number sets in functions, defining \(Z\) as integers and \(R\) as real numbers. It specifies \(Z^+\) for positive integers (counting numbers) and \(Z^+ \cup \{0\}\) for positive integers plus zero, noting that zero is neither positive nor negative.
  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/02%3A_Logic/2.04%3A_Mathematical_Proof
    This page discusses the concept of proof in mathematics, emphasizing its role in understanding and communication. It covers two theorems about sets: one states that the intersection of two sets is a s...This page discusses the concept of proof in mathematics, emphasizing its role in understanding and communication. It covers two theorems about sets: one states that the intersection of two sets is a subset of either, and the other indicates that the set difference is part of the complement of the second set. Both theorems include detailed proofs, along with practice checkpoints for further investigation.
  • https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/05%3A_Set_Theory
    Thumbnail: A Venn diagram illustrating the intersection of two sets. (Public Domain; Cepheus).
  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory/5.01%3A_Discovering_Graphs
    This page explains how to define graphs through various properties, using examples and checkpoints to distinguish valid graph formations from invalid ones. It employs set notation and prompts readers ...This page explains how to define graphs through various properties, using examples and checkpoints to distinguish valid graph formations from invalid ones. It employs set notation and prompts readers to analyze necessary and forbidden properties of graphs, facilitating a translation between set forms and diagrams.
  • https://math.libretexts.org/Courses/Hartnell_College/Mathematics_for_Elementary_Teachers/02%3A_Set_Theory
    The Manipulatives listed below are to be used with this workbook. You will be using the material cards to make your own manipulatives in order to do hands on activities in some of the exercise sets. Y...The Manipulatives listed below are to be used with this workbook. You will be using the material cards to make your own manipulatives in order to do hands on activities in some of the exercise sets. You should prepare them ahead of time, and keep each type of manipulative in its own baggie. The manipulatives to be used in an exercise set are listed at the beginning of that set. You should also have handy a calculator, scissors, tape, colored pencils, pens, markers, highlighters and/or crayons.

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