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21 votes

The action for this problem takes place in an island of Knights and Knaves, where Knights always make true statements and Knaves always make false statements and everybody is either a Knight or a Knave. Two friends A and B lives in a house. The census taker (an outsider) knocks on the door and it is opened by A. The census taker says ''I need information about you and your friend. Which if either is a Knight and which if either is a Knave?". "We are both Knaves" says A angrily and slams the door. What, if any thing can the census taker conclude?

  1. A is a Knight and B is a Knave.
  2. A is a Knave and B is a Knight.
  3. Both are Knaves.
  4. Both are Knights.
  5. No conclusion can be drawn.
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3 Answers

Best answer
31 votes
31 votes

Option (B) should be the correct answer, that is A is a Knave & B is a Knight.

A must be either a Knight or a Knave.


Suppose A is a Knight, it means that the statement "We are both Knaves." must be true.

This is contradicting our assumption.

So the assumption that "A is a Knight" is not logically satisfiable simultaneously with the statement he made, which implies that A must be a Knave.


Now since A is a Knave, the statement made by him : "We are both Knaves." must be false.

The statement "We are both Knaves." will be false in any one of the following 3 conditions :

  1. A is a Knight, B is a Knave.
  2. A is a Knave, B is a Knight.
  3. A is a Knight, B is a Knight.

Bus since we have already deduced that A is a Knave so in order to make the statement "We are both Knaves." false, we are only left with condition 2.

So B must be a Knight.

0 votes
0 votes

The statement “we both are knaves” can be interpreted as “A is knave and B is knave”

$\therefore $ $A$ is knave and $B$ is knight which is Option $\LARGE B$

–2 votes
–2 votes

Option (B) "A is a Knave and B is a Knight " is correct ans.

Answer:

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