Final answer:
By using logical deduction based on the given constraints, it is determined that person E and person C were selected for the school board positions.
Step-by-step explanation:
To solve this logic puzzle, we must analyze the given statements and use the process of elimination:
- If either A or F won a position, then G won a position.
- If neither D nor G won a position, then B won a position.
- If either B won a position or H did not win a position, then C won a position.
- D cannot win a position unless E also won a position.
Given that the school board must be composed of one man and one woman, let us consider that D cannot win unless E wins. Since only one woman can win, if E does not win, then D also does not win. Assuming D does not win, and following statement 2, B must win. If B wins, following statement 3, C also wins.
However, the board must consist of one man and one woman, and since B and C cannot both win as they are both men, our initial assumption that E does not win must be wrong. Therefore, E must win. If E wins, D is eligible to win but not certain to win.
Now let's consider the women. If E has won, A cannot win, or else G would also have to win, which isn't possible as only one woman can win. Hence, by statement 1, A and F cannot win. Since B also cannot win because E is already the winning woman, then by elimination, the winning man can only be C.
Thus, the two people selected to the school board are E and C.