Please be as detailed as possible Prove that the following is an equivalence rel

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Please be as detailed as possible

Prove that the following is an equivalence relation. Let S be the set of subsets of the real numbers R; we say that two such subsets s and t are equivalent if they differ in a finite number of elements. For example, letting s fodd numbers and t numbers divisible by 50, s and t are not equivalent because there are infinitely many odd numbers not divisible by 5. On the other hand, letting s (x E IN x 2 5) and t 3 (x N x 100), s and t are equivalent because the difference is the set of all natural numbers between 5 and 99, which is a finite set

Explanation / Answer

I have written the answer on a paper and uploaded it as 2 pictures at the following links:

PArt-1: http://i.imgur.com/9g0Swpt.jpg

Part-2: http://i.imgur.com/XY3jR40.jpg

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