Hey can anyone help me with this mathematical reasoning ques

Hey can anyone help me with this mathematical reasoning questions using deduction?

A very special island is inhabited only by knights and knaves. Knights always

tell the truth, and knaves always lie.

You meet seven inhabitants: Mel, Joe, Zed, Bart, Marge, Bozo and Carl.

Mel claims, \\Bart is a knight and Bozo is a knave.\" Joe claims that only a knave

would say that Marge is a knave. Zed claims that at least one of the following is

true: that Bart is a knight or that Bozo is a knave. Bart says that both Mel is

a knight and Zed is a knave. Marge tells you, \\Mel is a knave.\" Bozo tells you

that Carl is a knave. Carl says, \\Bozo is a knave or Bart is a knave.\"

Can you determine who is a knight and who is a knave?y

1. Determine, as best you can, which of the seven inhabitants is a Knight and which is

a Knave.

Could you also please show me the reasoning behind it?

Solution

Here if Bart is knight then zed is knave that means zed statement is false that bart is a knight or bozo is a knave. So clearly Bart is not knight or he is a knave. Again Joe claims that any one who says that Marge is a knave, is a knave

and no one says anything about Marge, that means MARGE is knight. And Marge is sayin that Mel is a knave.

Further carl and bozo both are saying knave to each other. That means both are knave.

So clearly MARGE IS knight here and Mel is a knave.

Answer