- #1
Ethers0n
- 27
- 0
1.From the problem statement
Let Z+ be the set of all positive integers; that is,
Z+ = {1,2,3,...}
Define Z+ x Z+ = {(a1, a2) : a1 is an element of Z+ and a2 is an element of Z+ }
2. If S is contained in Z+ and |S| >=3, prove that there exist distinct x,y that are elements of S such that x+y is even.
3. I need some help on where to start as I'm quite lost.
I can see how this would be true. for example the set S = {1,2,3,4}
The pairs (1,3) and (2,4) both satisfy the condition of x+y being even.
the are extensions of this homework problem as well, but I'm having trouble with the first bit...
Let Z+ be the set of all positive integers; that is,
Z+ = {1,2,3,...}
Define Z+ x Z+ = {(a1, a2) : a1 is an element of Z+ and a2 is an element of Z+ }
2. If S is contained in Z+ and |S| >=3, prove that there exist distinct x,y that are elements of S such that x+y is even.
3. I need some help on where to start as I'm quite lost.
I can see how this would be true. for example the set S = {1,2,3,4}
The pairs (1,3) and (2,4) both satisfy the condition of x+y being even.
the are extensions of this homework problem as well, but I'm having trouble with the first bit...