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Finite math problems

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32. Is it possible for two nonempty sets to have the same intersection and union? If so,
give an example

Let U = {2,3,4,5,7,9}; X= {2,3,4,5}; Y={3,5,7,9}; and Z= {2,5,4,7,9}. List the members of each set using set brackets.

a. In Example 6, what set do you get when you calculate ? (A ᴒ B) (A ᴒ B')?
b. Explain why in words (A ᴒ B) (A ᴒ B') = A

Let U = { All students in this school}; M = {All students taking this course}; N = {All students taking accounting}; P= {All students taking zoology}.

Here is example 6


Let B = {a,b,c,{d}, {e,f} }. Answer the following as true or false.

A. a ∈ B
b. {b,c,d} ⊂ B
c . {d} ∈ B
d. {d} ⊆ B
e . {e,f,} ∈ B
f . {a,{e,f} } ⊂ B
g. {e,f} ⊂ B

64. Electoral College U.S. presidential elections are decided by the Electoral College, in which each of the 50 states, plus the District of Columbia, gives all of its votes to a candidate.? Ignoring the number of votes each state has in the Electoral College, but including all possible combinations of states that could be won by either candidate, how many outcomes are possible in the Electoral College if there are two candidates? (Hint: The states that can be won by a candidate form a subset of all the states.)

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