Give 4 examples of established sets of numbers used in Mathematics (integers for example). Describe each set and give examples

  1. Give 4 examples of established sets of numbers used in Mathematics (integers for example).  Describe each set and give examples. 
  2. Create a universe of elements (use numbers, letters or anything else) and sets A, B, C and D out of the elements in your universe (have your sets overlap, otherwise they won’t be very interesting to operate on).  Perform the following set operations:
  3. A’
  4. A U B
  5. B ∩ C
  6. C – D
  7. A U (B ∩ C)
  8. (C ∩ D)’
  9. Demonstrate using your universe De Morgan’s Laws.  For both laws, perform the set operations on each side of the equals sign to show that they produce the same result.
  10. For a-f, write out the set operations in plain language (i.e. A intersect B).
  11. Chose two from a-f and draw a Venn diagram to represent the set operation.  Make sure to shade the portion of the diagram that set operation represents.
  12. Determine the set produced in a-f with the highest cardinality

Bonus:  Consider the following.

Invention                            Date      Inventor              Nation

Adding Machine               1642       Pascal                    France

Barometer                          1643       Torricelli               Italy

Electric razor                      1917       Schick                    US

Fiber optics                         1955       Kapany                 England

Geiger counter                  1913       Geiger                  Germany

Pendulum clock                1657       Huygens              Holland

Radar                                    1940       Watson-Watt     Scotland

Telegraph                            1837       Morse                   US

Thermometer                   1593       Galileo                  Italy

Zipper                                   1891       Judson                  US

Let this information represent U.  A = the set of items invented in the US.  B = the set of items invented after 1800 and C = the set of items that work based on mechanical energy only (a quick bit of research may be needed, n(C) = 3 although you could argue 4 or 5).

Determine the following:

[(A∩B) U (B∩C) U (C∩A) – (A∩(B∩C))