The action for this problem takes place in an island of Knights and Knaves 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 of you, is a Knight and which, if either of you, is a Knave?" "We are both Knaves" says A angrily and slams the door. What, if any thing can the census taker conclude? a.A is a Knight and B is a Knave. b.A is a Knave and B is a Knight. c.Both are Knaves. d.Both are Knights. e.No conclusion can be drawn. Not able to grasp it please someone help me

"a.A is a Knight and B is a Knave."

Then that'd be a lie. Knights can't lie so this is impossible.

"b.A is a Knave and B is a Knight."

That'd be a lie. Knaves lie. This is possible.

"c.Both are Knaves."

Then that'd be the truth. Knaves can't tell truth so this is impossible.

"d.Both are Knights."

Then that'd be a lie. Knights can't lie so this is impossible.

....

but to do it directly.

If "we are both knaves were true" then A is knave telling the truth. That's impossible so it is a lie. So A is lying so A is a knave. But as it is a lie they are not both knaves. So B is not a knave. So B is a knight.