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March 10th, 2011, 01:19 PM   #1
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Set Statements

I would appreciate help with the following problem:

A := {3x : x is an element of the Natural numbers}
B := {3x+21 : x is an element of the Natural numbers}
C := {x+7 : x is an element of the Natural numbers}
E := {x : x is an element of the Natural numbers}
F := {3x-21 : x is an element of the Natural numbers}

Are the following statements true? Need proof or why it is false.

A intersect E = B

A intersect C = B

E intersect F = A


Thanks for the help!
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March 10th, 2011, 01:23 PM   #2
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Re: Set Statements

A is a subset of E, so A^E (intersect) is just A.
Now the question is reduced to "A = B". They are not equal. Look for the smallest elements of each, and demonstrate that there is an element in (either A or B) that is not in the other.
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March 10th, 2011, 02:00 PM   #3
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Re: Set Statements

Moved to Set Theory.
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