From [2] and [3], either:
I. Mr. Aye won one game, Mrs. Aye won one game, and Mr. Bee won one game; or
II. Mr. Aye won two games and Mrs. Aye won one game; or
III. Mr. Aye won two games and Mrs. Bee won one game.
If I is correct, then [1] and [4] , Mr. Bee beat Mrs. Bee in the first game. Then, from [4], only Mr. Bee could have lost to Mr. Aye or Mrs. Aye in the second game. Then from [1] and [4], no one could have played against the last winner in the last game. So I is not correct.
II cannot be correct from [1] and [4].
so III is correct. If Mrs Bee won the first game, then she beat Mr. Bee in that game, from [1]. But then from [1] and [4], no one could have played against Mr. Aye in the second game. So Mr. Aye won the first game against Mrs. Aye, from [1]. Then , from [4], Mr Aye beat Mr. Bee in the second game . Then from [4], Mrs. Bee beat Mr. Aye in the third game.
So only Mrs. Bee did not lose a game.
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