- Give 4 examples of established sets of numbers used in Mathematics (integers for example). Describe each set and give examples.
- 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:
- A U B
- B ∩ C
- C – D
- A U (B ∩ C)
- (C ∩ D)’
- 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.
- For a-f, write out the set operations in plain language (i.e. A intersect B).
- 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.
- 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))