Homework 1 1) Give 4 examples of established sets of numbers used in Mathematics (integers for example). Describe each set and give examples. Label each set and describe the relationship between using...

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Homework 1 1) Give 4 examples of established sets of numbers used in Mathematics (integers for example). Describe each set and give examples. Label each set and describe the relationship between using either subset notation or a Venn diagram. 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: a. A’ b. A U B c. B ∩ C d. C – D e. A U (B ∩ C) f. (C ∩ D)’ g. 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. h. For a-f, write out the set operations in plain language (i.e. A intersect B). i. 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. j. Determine the set produced in a-f with the highest cardinality Bonus: Consider the following. InventionDateInventorNation Adding Machine1642PascalFrance Barometer1643TorricelliItaly Electric razor1917SchickUS Fiber optics1955KapanyEngland Geiger counter1913GeigerGermany Pendulum clock1657HuygensHolland Radar1940Watson-WattScotland Telegraph1837MorseUS Thermometer1593GalileoItaly Zipper1891JudsonUS 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))
Answered Same DaySep 11, 2021

Answer To: Homework 1 1) Give 4 examples of established sets of numbers used in Mathematics (integers for...

Rajeswari answered on Sep 11 2021
145 Votes
Homework 1
1) Give 4 examples of established sets of numbers used in Mathematics (integers for exam
ple). Describe each set and give examples. Label each set and describe the relationship between using either subset notation or a Venn diagram.
R = set of real numbers (includes rational, irrational numbers)
Q = Set of rational numbers ( numbers of the form p/q where p and q are integers and q ≠0)
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:
Let us say U = {1,2,3,4,5,6,7,8,9,10,11,12}
A = {1,3,5,7,9,11}
B = {2,5,7,11}
C = {3,6,9,12}
D= {2,4,6,8,10,12}
a. A’ = U-A = {2,4,6,8,10}
b. A U B = {1,2,3,5,7,9,11}
c. B ∩ C = common to both = {} (null...
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