A ski club is having an election for president. There are three candidates and 15 voters. Each voter casts a ballot listing his or her preferences for the candidates. Just before the winner is to be announced, the previous president announces that the preference table has been lost. The only information he can remember from the preference table is that there were only two columns in the table.

(a) Explain why there must be a majority winner.

(b) Explain why there must always be a majority winner, regardless of the number of candidates, when all voters vote, when there are an odd number of voters and only two columns in the preference table.