Problem #1 below is just for practice. Its standard sample solution via truth ta

Question

Problem #1 below is just for practice. Its standard sample solution via truth table appears below. Problem #2 is due for homework, at the start of class, on Thursday, Feb. 11.

Persons A, B, C below are natives of the Island of Knights and Knaves. Each native is either a knight or a knave, not both. Each full-sentence statement uttered by a knight is true. Each full-sentence statement uttered by a knave is false. In each problem below, use a standard truth table for this situation to determine all possible combinations of types for the natives within each separate problem. It is possible for such a problem to have just one combination possible, several combinations possible, or no combinations possible.

#1:

A says: I am a knight or B is a knave.

B says: I am a knight or A is a knight, but not both.

#2:

A says: None of us are knights.

B says: But I am a knight.

C says: If B is a knight, I am a knave.

Solution to #1:

Statement 1: A is a knight or B is a knave.

Statement 2: B is a knight or A is a knight, but not both.

A is a

knight

B is a

knight

1

2

1 is

consistent

2 is

consistent

1

1

1

0

1

0

1

0

1

1

1

0

0

1

0

1

1

1

0

0

1

0

0

1

A is a knave and B is a knight (the only possible combination of types).

Please solve B according to the example A

A is a

knight

B is a

knight

1

2

1 is

consistent

2 is

consistent

1

1

1

0

1

0

1

0

1

1

1

0

0

1

0

1

1

1

0

0

1

0

0

1

Explanation / Answer

Statement 1: None of us are knights.

Statement 2: But I am a knight.

Statement 3: If B is a knight, I am a knave.

A is a

knight

B is a

knight

C is a

knight

1 is

consistent

2 is

consistent

3 is

consistent

A is knave,.

B is knave.

C is knight.

A is a

knight

B is a

knight

C is a

knight

1 2 3

1 is

consistent

2 is

consistent

3 is

consistent

1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0

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