Everyone is either a knight or a knave Everyone is either a knight or a knave. Knights always tell truth, knaves always lie. Alice says: Bob is a knight. Bob says: Alice and I are of opposite. Determine what each is.

a b [A] b [B] (a~b)(~ab) (aA)(~a~A) (bB)(~b~B) T F a: Alice is a knight b: Bob is a knight A: What Alice says is the truth B: What Bob says is the truth Solution Both Alice and Bob are Knaves.

Everyone is either a knight or a knave Everyone is either a knight or a knave. Knights always tell truth, knaves always lie. Alice says: Bob is a knave, or Chris is a knight. Chris says: Alice is a knave. Determine what each is.

a b c [A] ~bc [C] ~a (aA)(~a~A) (cC)(~c~C) T F a: Alice is a knight; b: Bob is a knight; c: Chris is a knight A: What Alice says is the truth; C: What Chris says is the truth Solution: Alice is a knight; Bob is a knaves; Chris is a knave.

If this house is next to a lake, then the treasure is not in the kitchen. If the tree in the front yard is an elm, then the treasure is in the kitchen. This house is next to a lake. The tree in the front yard is an elm or the treasure is buried under the flagpole. If the tree in the back yard is an oak, then the treasure is in the garage. Where is the treasure?

All writers who understand human nature are clever. No one is a true poet unless he can stir the human heart. Shakespeare wrote Hamlet. No writer who does not understand human nature can stir the human heart. None but a true poet could have written Hamlet.  Shakespeare was clever.

All writers who understand human nature are clever. ∀x, if x is a writer who understands human nature, then x is clever.

2. No one is a true poet unless he can stir the human heart 2. No one is a true poet unless he can stir the human heart. No one is a true poet if not he can stir the human heart. No one is a true poet if he cannot stir the human heart. No person who cannot stir the human heart is a true poet. ∀x, if x is a person who cannot stir the human heart, then x is not a true poet. ∀x, if x is a true poet, then x is a person can stir the human heart. ∀x, if x is a true poet, then x can stir the human heart.

3. Shakespeare wrote Hamlet. 4 3. Shakespeare wrote Hamlet. 4. No writer who does not understand human nature can stir the human heart. ∀x, if x is a writer who does not understand human nature, then x cannot stir the human heart. ∀x, if x can stir the human heart, then x is a writer who understands human nature.

5. None but a true poet could have written Hamlet 5. None but a true poet could have written Hamlet. No person who is not a true poet could have written Hamlet. ∀x, if x is a person who is not a true poet, x could not have written Hamlet. ∀x, if x have written Hamlet, then x is a person who is a true poet. ∀x, if x have written Hamlet, then x is a true poet.

All writers who understand human nature are clever. No one is a true poet unless he can stir the human heart. Shakespeare wrote Hamlet. No writer who does not understand human nature can stir the human heart. None but a true poet could have written Hamlet. ∀x, if x is a writer who understands human nature, then x is clever. ∀x, if x is a true poet, then x can stir the human heart. Shakespeare wrote Hamlet. ∀x, if x can stir the human heart, then x is a writer who understands human nature. ∀x, if x have written Hamlet, then x is a true poet.