I need somebody who really understands the material. Please only apply if you can really do this math. If you are not sure, please do not waste my time - I will give you a bad review if things are wrong.

The total number of points is 10. Your total score will be divided by 10 to produce a

score over 100. Show all work.

1

Describe the following set by listing its elements:(1 point)

{x | x ∈ N and x is even and 2 < x < 11}

2

Describe the following sets by giving a characteristic property:

1. {1,3,5,7,9,11, ...} (1 point)

12. {2,4,8,...} (1 point)

3

What is the cardinality of each of the following sets:

1. S={Ø ,{Ø,{Ø}},{Ø,{Ø,{Ø}}}} (1 point)

2. The power set℘(S) where S is a set of 15 elements (1 point)

4

Let A={1,2,4,7,8} and B={7,8}

Is the statement B ⊆A true? Explain. (1 point)

5

Find the power set℘(S) for S={Ø,{Ø},{Ø{Ø}}} (1 point)

6

1. What can be said about A if℘(A)={Ø,{x},{y},{x, y}}? (1 point)

2. What can be said about A if℘(A) = {Ø,{a},{{a}}}? (1 point)

7

A, B, and C are subsets of a set S. Prove the following set identity using the laws of set

theory (set identities). Justify each step with the law you used.

(A ∪ C) ∩ [(A ∩ B) ∪ (C’ ∩ B)] = A ∩ B (1 point)

Subject | Mathematics |

Due By (Pacific Time) | 10/25/2014 12:00 am |

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