I just need the answers to this homework sheet asap.

Math 107 Logic Puzzles and Truth Tables Spring 2020

Suppose you travel to a funny place where everyone either tells the truth all the time or they lie all the time (and they do not change). Let’s call them type T and type F. Two inhabitants, A and B, approach you and A says: “Both of us always lie.”

Follow the steps below to determine whether A is type F or Type T.

Step 1 (5 pts): Fill in all the possible truth values in the “A is T” column. Note that “A is T” is the statement that “inhabitant A is of type T.” So, when you place a “F” under that heading then you are saying for that row that the statement is false, which means that inhabitant A is of Type F.

Step 2 (5 pts): Fill in all the possible truth values in the “B is T” column.

Step 3 (5 pts): Fill in all the possible truth value in the “A is F AND B is F” column based on your answers to steps 1 and 2.

Step 4 (5 pts): Fill in the final column. Put a “T” if the values in “A is T” and “A is F AND B is F” match, otherwise put an “F”. There will be only one cell that is “T”. On this row what is the truth value of “A is T”? Is inhabitant A type F or Type T?