help with truth tables

• Oct 3rd 2006, 03:49 PM
chickenwing
help with truth tables
Translate the following argument into symbolic form and determine whether it's logically correct by construcing a truth table.

If the team wins, then the team remains in the playoffs. If the team stays in the playoffs, then the championship is in reach. Therefore, if the team wins, the championship is within reach.
• Oct 3rd 2006, 04:23 PM
OReilly
Quote:

Originally Posted by chickenwing
Translate the following argument into symbolic form and determine whether it's logically correct by construcing a truth table.

If the team wins, then the team remains in the playoffs. If the team stays in the playoffs, then the championship is in reach. Therefore, if the team wins, the championship is within reach.

Well, we can transform these sentences into symbols.

Lets say
A = "team wins"
B = "team remains (stays) in the playoffs"
C = "championship is in reach"

So, we have A -> B, B -> C and [(A -> B) AND (B -> C)] -> (A -> C).

So, construct table with columns A,B,C, A -> B, B -> C, A -> C and [(A -> B) AND (B -> C)] -> (A -> C) and put every value true or false for A,B,C and fill A -> B, B -> C, A -> C and [(A -> B) AND (B -> C)] -> (A->C) according to logical rules.