5 votes 5 votes An island has two kinds of inhabitants, knights, who always tell the truth, and knaves, who always lie. You encounter two people $A$ and $B$. What are $A$ and $B$ if: $A$ says “$B$ is a knight” and $B$ says “The two of us are opposite types”? $A$ is knight, $B$ is knight $B$ is knight, $B$ is knave. $A$ is knave, $B$ is knave.$A$ is knave, $B$ is knight Mathematical Logic goclasses goclasses_wq3 mathematical-logic propositional-logic 2-marks + – GO Classes asked Mar 23, 2022 retagged May 1, 2022 by Lakshman Bhaiya GO Classes 565 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes Assume $A$ is knight then $B$ is also knight But now according to $B$, “The two of us are opposite types” should be true But it is Not true. So, $A$ is knave, so, according to $A$ “$B$ is a knight”, should be a lie, so $B$ is knave. GO Classes answered Mar 23, 2022 edited Mar 24, 2022 by soujanyareddy13 GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Knights : x : TRUE wala. Knaves : y: FALSE wala. A: “B is x” B: “Opposite” Option A : A is x & B is x? As A is x: which means he is true → B is x As B is given/proven to be x → A must be y: CONTRADICTION: HENCE OPTION A IS FALSE Option B : A is x & B is y? As A is x: which means he is true → B is x: CONTRADICTION: HENCE OPTION B is also FALSE Option C : A is y & B is y? A is y → which means A is false → B is y B is y → which means B is false → A is y HENCE TRUE Udhay_Brahmi answered Aug 19, 2022 Udhay_Brahmi comment Share Follow See all 2 Comments See all 2 2 Comments reply Udhay_Brahmi commented Aug 19, 2022 reply Follow Share @Deepak Poonia sir : Please confirm this. 0 votes 0 votes Deepak Poonia commented Aug 19, 2022 reply Follow Share @Udhay_Brahmi It’s correct But making two cases is more efficient. Being efficient is also important. 0 votes 0 votes Please log in or register to add a comment.