Question

Four men and four women were nominated for two positions on the school board. One man and one woman were selected to the positions. Suppose the four men are named A, B, C, and D and the women are named E, F, G, and H. Further, suppose that the following statements are true: If neither C nor F won a position, then H won a position; If either C won a position or G did not win a position, then B won a position but F did not win a position. Who were the two people elected to the school board and why?

Answer 1

Using logic and considering the given statements, we can deduce that B and H are the two people elected to the school board. The reasoning involves eliminating the possibilities where conditions contradict the given rules, arriving at B and H as consistent with all provided conditions.

Step-by-step explanation:

To determine who were the two people elected to the school board, we must use the given conditional statements to deduce the possible winners.

First, let's consider the statement, 'If neither C nor F won a position, then H won a position.' Since one man and one woman must win, this means that if C did not win, then neither did F, which would ensure H's victory. However, regarding the second statement, 'If either C won a position or G did not win a position, then B won a position but F did not win a position,' this suggests B must win if C wins or if G does not win.

Now let's analyze the possibilities. For H to win, neither C nor F can win, but if C doesn't win, B must win according to the second condition. So, if B wins, C cannot win, as they are both men.

However, for B to win, C has to win or G must not win. As C winning contradicts B's win (they can't both win), this means G must not win, thus clarifying that out of the women, F doesn’t win either according to the second statement. Therefore, the two people who must have been elected to the school board are B and H.