In which subject the overall percentage is the best?

Mr. Baha Man had locked his pet dogs in his room and instructed his three sons – Woof, Arf and Grrr – to keep a watch over them while he was away. When he came back, he found that there were no dogs in the room. When he came to know that exactly one of his sons had let the dogs out, he angrily shouted at them, “WHO LET THE DOGS OUT?” Frightened, each son gave two replies to the question, as given below:
Woof : Arf did. Grrr didn’t.
Arf : I didn’t. Woof did.
Grrr : Woof didn’t. Arf didn’t.
If it is known that of the statements given by each son at least one was true, then which son let the dogs out?

Each of three players A, B and C are selected to play for their college in exactly one game among Badminton and Chess. Atleast one person is selected for each game. Further it is known that:
If A is selected for Badminton, then B is not selected for the game for which C is selected.
If B is selected for Badminton, then A not selected for the game for which C is selected.
If C is selected for Chess, then A selected for the game for which B is selected.
Which of the following cannot be true of the final selection?