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In: Advanced Math

Solve the following logic problems. Remember, everyone you meet is either a knight or a knave,...

Solve the following logic problems. Remember, everyone you meet is either a knight or a knave, knights make true statements, and knaves make false statements. Give your reasoning for each problem. p,q,r and T/F truth table format.

You meet two residents, Alex and Bill. They say the following: Alex: I’m a knight. Bill: Alex is a knight, but I’m a knave. Is Alex a knight or a knave? Is Bill a knight or a knave?

You meet Clara and Davis, who are all like: Clara: One of us is a knight and the other is a knave. Davis: Clara is a knave. Is Clara a knight or a knave? Is Davis a knight or a knave?

You meet Edith and Frank, though only Edith speaks. Edith: Both Frank and I are knaves. Is Edith a knight or a knave? Is Frank a knight or a knave? (Note: Frank’s silence gives no indication of his type, but you can figure out from Edith’s statement.)

You meet Gina, Herbert, and Ichabod. Gina: Ichabod is a knave, if and only if I’m a knight. Herbert: Ichabod is a knight, if and only if I’m a knave. Ichabod: I like pudding. Does Ichabod like pudding?

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