MATC1100

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Author:
insouci
ID:
4347
Filename:
MATC1100
Updated:
2010-01-17 00:29:31
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TWC MATC 1100
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Description:
Ch. 1&2
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  1. What are the two types of reasoning we use in everyday life?
    • 1. Inductive reasoning
    • 2. Deductive reasoning
  2. inductive reasoning
    Inductive reasoning is the process of reasoning that arrives at a general conclusion or conjecture based on the observation of specific examples.

    **Using specific examples to --- arrive --- at a general conclusion
  3. deductive reasoning
    Deductive reasoning is the process of reasoning that arrives at a specific conclusion based on previously accepted general statements.

    ** Arrive at a specific conclusion --- via --- previously accepted statements.
  4. George Polya
    FOUR major steps of problem solving
    • 1. Understand the problem
    • 2. Devise a plan
    • 3. Carry out the plan
    • 4. Look back, check the work
  5. estimation
    Estimation is the process of finding an approximate answer to a mathematical problem.

    In many cases, it is not necessary to find the exact answer to a problem. When only an approximate answer is needed, you can use estimation. This is accopmplished by rounding the numbers used in the problem, then performing the necessary operatioin or operations.
  6. define a set
    A set is a well-defined collection of objects/elements.
  7. What is meant when a set is well defined?
    A set is said to be well defined when there is no misunderstanding as to whether or not an element belongs to a set.

    Ex:the set of "letters of the English alphabet" is a well-defined set since it consists of the 26 symbols.

    • The set of Great Lakes is {Ontario, Erie, Huron, Michigan, Superior}
    • The days of the week are {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
    • Write the set of natural numbers less than 6 {1, 2, 3, 4, 5}
  8. Name the 3 ways to designate sets
    • 1. list or roster method
    • 2. descriptive method
    • 3. set-builder method
  9. Each object of a set is called...
    an element or member of the set.
  10. Write the set of natural numbers less than 8.
    {1, 2, 3, 4, 5, 6, 7}
  11. Write the descriptive of the set containing 2, 4, 6, 8, ...
    Since the elements in the set are called the even natural numbers, the anser is:

    E = even natural numbers
  12. Use set-builder notation to designate the set {2, 4, 6}
    { x | x E and x < 7 }

    Reads: "The set of all x such that x is an even natural number and x is less than seven."
  13. Use set-builder notation to designate the set {red, yellow, blue}
    {x | x is a primary color}

    Reads: "The set of all x such that x is a primary color."
  14. Designate the set 32, 33, 34, 35, ... using the roster method.
    {32, 33, 34, 35, ...}
  15. Designate the set 32, 33, 34, 35, ... using the descriptive method.
    Natural numbers greater than 31.
  16. Designate the set 32, 33, 34, 35, ... using the set-builder notation.
    { x | x N and x > 31 }
  17. finite set
    A set is said to be a finite set if the number of elements contained in the set is either 0 or a natural number.
  18. infinite set
    A set is said to be an infinite set if it has an unlimited number of elements.
  19. finite? or infinte?

    {the natural numbers that are multiples of 6}
    infinite
  20. finite? or infinte?

    { x | x is a member of the U.S. Senate}
    finite
  21. finite? or infinte?

    {3, 6, 9, ..., 24}
    finite
  22. null set
    A set with no elements is called an empty set or null set. The symbols used to represent the null set are { } or circle w/line
  23. Two sets are equal if...
    they have exactly the same members or elements.
  24. Two sets have a one-to-one correspondence if and only if...
    it is possible to pair the elements of one set with the elements of the other set in such a way that for each element in the first set there exists one and only one element in the second set.
  25. What is a subset?
    When all, some, or none of the elements of one set are used in another set, the second set is called a subset of the original set. Formally defined.

    Ex: Subsets of {bacon, egg}

    • {bacon, egg}
    • {bacon}
    • {egg}
    • { }
  26. What is a proper subset?
    If a subset of a given set is NOT equal to the original set, then the subset is called a proper subset of the original set.

    Original set: {bacon, egg}

    {bacon, egg} ⊄ {bacon, egg} **Because it is equal to the original

    {bacon}⊂ {bacon, egg}
  27. What is the union of two sets?
    All the elements of each set. Duplicates are not written twice.

    Ex: A={10, 12, 14, 15} and B={13, 14, 15, 16, 17}

    A ∪ B={10, 12, 13, 14, 15, 16, 17}
  28. What is the intersection of two sets?
    The set of elements that are common to both sets.

    Ex: A={10, 12, 14, 15} and B={13, 14, 15, 16, 17}

    A∩ B = {14, 15}
  29. What is the complement of a set?
    • It is the set of elements contained in the universal set that are NOT contained in the set noted.
    • _
    • A (the line over the set name denotes the compliment of that set)
    • Basically everything outside of the mentioned set.
  30. What is a Venn Diagram?
    When a set or sets are represented pictorially using Venn Diagrams.

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