Statement A: Both fathers always tell the truth or both fathers always lie.

Statement B: One son always tells the truth and one son always lies.

Statement C: Statement A and Statement B are not both lies.

Here are a few facts given related to the statements above and the men who made them:

(i) Albert made one of the statements, his father made another of the statements, and his son made the remaining statement.

(ii) Each father and son mentioned in the statements refers to one of the three men.

(iii) Each man either always tells the truth or always lies.

Which statement – A, B or C – was made by Albert?

Starting with Statement C, This must be true:

If it were false, then it's negation must be true, and both Statements A and B must be false. If all three statements are false, then both fathers are liars, and Statement A is true.

So there are 3 possibilities: (1) A true, B true, C true; (2) A true, B false, C true; (3) A false, B true, C true

We can eliminate (1) because B leads to the contradiction that one son is a liar who made a true statement.

So we know that C is true, and either A is true and B false, or B is true, and A is false.

(2) If A is true, then both Albert and his father lie, or both tell the truth. Since there is only one false statement, both tell the truth, and Albert's son lies, and B is also true. This leads to the same contradicion as case (1)

(3) If B is true, then Albert and his son are opposite parity. Since A is false, Albert and his father are also opposite parity. Since there are 2 true statements and one false, then Albert is the liar. He made the false statement. Statement A is Albert's

Posted by TomM on 2003-01-28 02:50:54