please make answer small and to the point

1. [20 points] More proof techniques. 1a. [10 points] Suppose at a party (with at least two people), for each pair of people either they are friends with each other or they are enemies with each other. Give a proof by contradiction: Either everybody has at least one friend, or everybody has at least one enemy. 1b. [10 points] In a 2-dimensional table of blue and gray pebbles, call a column almost-blue when it has at most one gray pebble. Prove that for every table, (there are at least two almost-blue columns) iff (for every way of choosing two pebbles from each column, at least two of all the chosen pebbles are blue and in different columns)