1. Let us form two sets within the set of natural numbers. Set X with elements (2x, 2x+1) where 2x and 2x+1 are consecutive numbers. Let us consider another set Y with elements (2y, 4y) where x is not equal to y and 2y and 4y are not consecutive numbers. Now if we consider the combinations of addition between X and Y we get 2x+2y, 2x+4y, 2x+1 + 2y and 2x + 1 + 4y. Now if we substitute x=1 and y=2 we get 6, 10, 7 and 11. If we look at the term 2x+1 it is the only odd number in the two sets and it produces odd numbers when combined with an even number as in set Y. if we extend this concept we come to know that this is true for all numbers in set of natural numbers.  2.  4. No, I'm pretty sure you get it as well as anybody else does  5. That's what I thought it meant too.  6. Originally Posted by parag
When two odd numbers are added we get an even number.
When we add two even numbers we get an even number.
When we add one odd number and one even number we get an odd number.
Uh...before you proceed, you need to prove this assertion for all n in N.  7. If x are all odd and y are all even, then z are all odd and the intersection of z with any other set would have more odd numbers, not even. Unless I have totally misundrstood the original post.  Bookmarks
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