I like the approach you both have taken to Statement 2, but in case others didn't think of it that way, as I didn't, another approach to statement 2:
IF A,B,C AND D ARE INTEGERS. AND A/B AND C/D ARE INTEGERS. IS A/B + C/D ODD OR EVEN ?
II: AD + BC IS ODD
AD + BC must be E + O. Let's assume AD is the odd one, since the situation is the same either way.
Then, A is odd, D is odd, and at least one of B or C is even.
So, the numbers are either OOOE or OOEE
Now, if it were OOEE, either B or D would have to be even, which would mean that in the sum A/B + C/D we would be doing O/E in one of the terms, which would be impossible.
So, it must be OOOE, with either A or C as the sole even number.
So, A/B + C/D = E/O + O/O.
As others have noted, O/O = O and E/O = E, so the sum A/B + C/D = O.
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