Math set theory

Card Set Information

Math set theory
2013-05-04 15:18:35
math set theory relations power partitions union intersect cartesian product

A set of flash cards created for personal use based on the studies within a undergraduate computer science course
Show Answers:

  1. Name and describe the attributes of a set.
    • Element 
    • A word used to describe an object located within the set. For example given C={1,2,3...10} then any number from 1 to 10 is an element of C or more specifically 2 is an element of C.
    • Index
    • A means of understanding the range of the set. An example would be  A={for xEN | x>2}
    • Element A would include all natural integers greater than 2.
  2. What is a set?
    A set is collection of objects. These objects can be literal like furniture in a room or names of people who were famous or they can be more abstract such as numbers.
  3. What is a subset?
    A subset is a word to describe a set who's elements are found in another set. For example set A={1,2}  and set B={1,2,3} thus A is a subset of B and can be written as such  A c B.
  4. Describe the word compliment in relation to sets.
    If a set F={1,2,3} then F complement will contain all numbers that are not in F. We can illustrate a compliment with a tiny above the set name.
  5. What is the compliment of set A=R (R is a set of all numbers)
    The empty set or  Ac={0}
  6. What is a Cartesian product?
    A means of relating 2 elements from to 1 element within a set.
  7. What is a power set?
    • A set of subsets against a given set as such given set A={1,2,3} then
    • P(A)={0,(1),(2),(3),(1,2),(1,3),(2,3),(1,2,3)}
    • The power set will always have 2^(number of elements for a given set)
  8. Describe 3 kinds of set classifications (These are based on how the elements relate to one another within the set).
    • Reflexive
    • For where in a set there exists x then there must exist y as such it is equal to x.

    • Symmetry
    • For where in a set there exists x and y then there must exist for elements  y and x.

    • Transitivity
    • For where in a set there exists x and y then there is y and x and so x and z.
  9. Describe set union and intersect.
    • Union
    • The grouping of all unique elements from 2 or more sets to form a new set.

    • Intersect
    • The grouping of elements from 2 or more sets where the elements are found in all sets.