Mathematics in the modern world

    Cards (44)

    • Statement describing the common characteristics, properties, or features of the elements in the set
      Rule Method/Defining Property Method
    • A={x/x is one of the first three positive even integers}
      Set-builder notation
    • Illustrates sets using simple closed curves, usually circles in a plane. These curves represent the sets. The concept was introduced by the swiss mathematician Leonhard Euler.
      Euler's diagram
    • Classifications of Sets include...
      m
      1. Null Set
      2. Unit/Singleton Set Set
      3. Equal Set
      4. Equivalent Set
      5. Finite Set
      6. Infinite Set
      7. Joint Set
      8. Disjoint Set
      9. Universal Set
    • Subset - A subset of a set A is any set whose members are all members of A.
    • Infinite Set - A set that contains an infinite number of members.
    • Symbolized by {} or Φ
      A set which contains no members.
      Null Set
    • Set which has only one element
      Unit Set
    • Two sets having exactly the same elements(regardless of order)
      Equal Sets
    • Sets having the same cardinality
      Equivalent sets
    • Sets whose number of elements can be counted
      Finite sets
    • Set containing elements that cannot be counted
      Infinite sets
    • Two sets with different elements
      Disjoint Sets
    • Sets containing or sharing an element
      Joint Sets
    • Set containing all the elements in the discussion
      Universal Set
    • Operations on sets and their venn diagram includes...
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      1. Union of Sets
      2. Intersection of Sets
      3. Complement of Sets
      4. Difference of Sets
      5. Symmetric Difference of Sets
      6. Cartesian Product
      7. Power set of A (p((a))
    • Set whose elements are found in both Set A and B
      UNION OF SETS
    • Set whose elements are found in both Set A and B: ∧ means "and"
      Intersection of Sets
    • Set whose elements found in Universal set(U) but not in A
      Complement of a Set
    • Set whose elements are found in A but not in B
      ∉ means not an element of
      Difference of Sets
    • Set whose elements are contained in the union of A and B but not in the intersection of A and B
      The Symmetric difference of sets
    • Set whose elements are expressed in an ordered pair
      Cartesian Product
    • Set whose elements are the subsets of a given Set
      Power set of A (p((a))
    • A relation is a correspondence between two things or quantities. It is a set of two ordered pairs where each element in the first set, called the domain(input), corresponds to at least one element in the second set, called the range(output). A relation is a set of ordered pairs.
    • A function is a special type of relation where each x value is related to only one y value. To identify a function from a relation, check to see if any of the x values are repeated - if not, it is a function.
      It can be a one-to-one or one-to-many correspondence
    • Binary operation on a set S is an operation that combines the elements of the two sets to produce one element, that belongs to set S.
      The four arithmetic operations are the basic binary operations. Union and intersection are binary operations.
    • Elementary logic forms the foundation of reasoning and problem solving in several fields. It deals with logical statements and propositions using connectives, quantifiers, negations and variables
    • Propositions are statements that can either be true or false. It is used to express facts that can be evaluated using a truth table.
    • Truth Table is a device that allows us to compare and analyze compound logic statements.
    • The letters we use to represent the propositions or statements are called the variables
    • m
      A) if then(T->F=T)
    • ∧ Only true If both are true else, false.
      ∨ Only false If both False else, true
      ⇒ If True first then False, then it is true. Else, False
      If both are same then T or F (TT=T/FF=F)
    • Connectives are called compound prepositions
      Examples are: And, Or, If and only If, and If then
    • Quantifiers are words such as:
      All
      None
      Some or at least one
      The symbolis called the universal quantifier.
      The symbolis called the existential quantifier.
    • If all the final values resulted to true, this is called tautology
    • If q is a statement then not q is a negation
    • If p then q is a conditional statement
    • converse is the reverse of the conditional statement.
      If q then P
    • if the converse is true and the conditional statement is true, then it is biconditional statement
    • Inverse is simply the negation of the conditional statement
      If not p then not q