Question regarding Proofs  TOPIC_SOLVED

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Question regarding Proofs

Postby CaptainCornbread on Sun Jul 17, 2011 9:46 pm

I am working on a school assignment and I am being asked to solve the following:

Let A be the set of all integers x such that x is = k2 for some integer k
Let B be the set of all integers x such that the square root of x, SQRT(x), is an integer
Give a formal proof that A = B. Remember you must prove two things: (1) if x is in A, then x is in B, AND (2) if x is in B, then x is in A

I have done proofs before in my class that involved first proving that certain terms were odd or even and then algebraically reducing to a final proof, but I am not sure of how to go about proving this one. Any help will be appreciated. Thank you.
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Re: Question regarding Proofs  TOPIC_SOLVED

Postby nona.m.nona on Mon Jul 18, 2011 12:34 am

CaptainCornbread wrote:Let A be the set of all integers x such that x is = k2 for some integer k
Let B be the set of all integers x such that the square root of x, SQRT(x), is an integer
Give a formal proof that A = B. Remember you must prove two things: (1) if x is in A, then x is in B, AND (2) if x is in B, then x is in A

I have done proofs before in my class...but I am not sure of how to go about proving this one.

Try following the listed steps:

Pick an element of A. This is some number x = k2 for some integer k. What would be the value of sqrt{x}? Would this be an element of B? If every element of A is also an element of B, what sort of set is A with respect to B?

Then apply the same process in the other direction. What can you say about two sets which are subsets of each other?
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