Arminius wrote:Six people in two groups.

There are six people A, B, C, D, E, F which are in each case either in group 1 or group 2. The following statements are given:

1. Both A and B are in 1.

2. F is in 2, and if E is in 2, then C is also in 2.

3. D is in 1 and if F is in 2, then A is also in 2.

4. A and E are both in 2.

5. D is in 2 and E is in 1, and if C is in 2, then B is in 1.

6. D and B are both in 2.

7. The statements 1-6 are wrong.

Who is in which group?

1. A and B cannot both be in 1. Either A is in 1, B is in 1, or Neither are in one

Either A or B, or both A and B is in group 2.

2. F is undefined. E is undefined. C is undefined.

3. D is undefined. F is undefined. A is undefined.

4. Either A or E, or both A and E are in group 1.

5. D is undefined. E is undefined. C is undefined. B is undefined.

6. Either D or B, or both D and B are in group 2.

No solution.

If a statement is wrong, only one component may be wrong. Therefore, F is undefined.

For instance, in 2. F may be in 2, because only the end of the statment may be wrong. Therefore F is undefined