If Mr.M is guilty, then no witness is lying unless he is afraid. There is a witness who is afraid. Which of the following statements is true?
(Hint: Formulate the problem using the following predicates
G−Mr.M is guilty W(x)−x is a witness L(x)−x is lying A(x)−x is afraid )
a.Mr.M is guilty. b.Mr.M is not guilty. c.From these facts one cannot conclude that Mr.M is guilty. d.There is a witness who is lying. e.No witness is lying.
i am solving like this. a witness who is afraid if he asked about Mr. M's guiltiness he will lie that means we have found out someone who lying so Mr.is not guilty.can we do like this without hint?
The correct answer is
The statement in questoin is that $if\ Mr.M=guilty\to no\ witness\ is\ lying\ unless\ he\ is\ afraid.$ To illustrate this, let's look at another example.
If a polygon is a square, then it is a rectangle. Despite the fact that all squares are rectangles, the converse is not necessarily true. It is extremely easy to come up with a counterexample of a rectangle that is not a square.
Similar logic can be applied to the original question. Just because no witness lies unless he is afraid, that does not mean that Mr. M is guilty. Also, we don't know if the witness is lying. All it says is that he is afraid. This means no additional information can be gained from only knowing that a witness is afraid. Therefore, all other answers cannot be proven.