Kenneth Rosen Edition 6th Exercise 1.1 Question 44 (Page No. 20)

Question

Fuzzy logic is used in artificial intelligence. In fuzzy logic, a proposition has a truth value that is a number between 0 and 1, inclusive.A proposition with a truth value of 0 is false and one with a truth value of 1 is true. Truth values that are between 0 and 1 indicate varying degrees of truth. For instance, the truth value 0.8 can be assigned to the statement “Fred is happy,” because Fred is happy most of the time, and the truth value 0.4 can be assigned to the statement “John is happy,” because John is happy slightly less than half the time. Use these truthvalues to solve below Exercises.

An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road shaves those people, and only those people, who do not shave themselves. Can there be such a barber?

Answer 1

No. If such a barber existed then who would shave the barber? The barber cannot shave himself then he would be violating the rule that he shaves only those who don't shave themselves. Now if he doesn't shave himself then the rule says that he (the barber) must shave himself. None of these is possible so no such barber exists.                          

This question is not related to Fuzzy Logic at all.

Comments

That's already answered by you in first para. 

 the barber in a remote town  shaves those people who do not shave themselves

if the barber does not shave himself, he must shave himself. To make the implication true, here LHS must be false =>  he must shave himself.

 the barber in a remote town  shaves only those people who do not shave themselves

The only means that, barber cannot shave himself. So, such a barber cannot exist. 

 

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Got it sir...Edited the answer.

Thank you.

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I was really confused with this question. Finally, got it. Thanks.