Question

1. In a game, groups of 3 are competing. Each player of each group flips a coin only ONCE. A group will be announced winner only if either the first or the second player gets head (but not both) and the third player gets tail. Using P₁, P₂ and P₃ to represent player1, player2 and player3 respectively and logical connectives AND, OR and NOT, write a statement in which a group wins the game. Discuss your answer.   

Hint: Assume head has true and tail has false truth values.

Answer 1

Assuming :

head as True and tail as false.

A' indicates NOT of A

ABC indicates AND of A, B and C

A + B + C indicates OR of A, B and C

Case 1:

Player 1 gets head and the other two gets tail

We can write it as: P₁P'₂P'_{3 ^.} It means that this expression evaluates to true only when P₁ gives head and other two gives false.

Case 2:

Player 2 gets head and the other two gets tail

We can write it as: P'₁P₂P'_{3 ^.} It means that this expression evaluates to true only when P2 gives head and other two gives false.

Since any the above two cases will give us winner we can write final statement for a group to win as:

P₁P'₂P'₃ + P'₁P₂P'₃