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Nov 2 In-Class Exercise Thread.

Please post your solutions to the Nov 2 In-Class Exercise to this thread.

Best,

Chris

Please post your solutions to the Nov 2 In-Class Exercise to this thread. Best, Chris

-- Nov 2 In-Class Exercise Thread

 Universe = Domain: a, b, c, d
 Knows(a,a)
 Knows(b,b)
 Knows(c,c)
 Knows(d,d)
 Knows(a,b)
 Knows(b,c)
 Knows(a,d)

 x -> a, y-> d, z->b
 For_All(x) Knows(x,x) AND Exists(y)not Knows(z,y)

Universe = Domain: a, b, c, d Knows(a,a) Knows(b,b) Knows(c,c) Knows(d,d) Knows(a,b) Knows(b,c) Knows(a,d) x -> a, y-> d, z->b For_All(x) Knows(x,x) AND Exists(y)not Knows(z,y)

-- Nov 2 In-Class Exercise Thread

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-- Nov 2 In-Class Exercise Thread

 Let universe U = {"PersonA", "PersonB", "PersonC", "PersonD"}
 Knows := {("PersonA", "PersonA"), ("PersonB", "PersonB"), ("PersonC", "PersonC"}, ("PersonD","PersonD")}
 F := (∀x)Knows(x,x)∧(∃y)¬Knows(z,y)[z -> "PersonB"]
              T           ¬Knows(z,y)[z -> "PersonB", y -> "PersonA"]
                                F
                       T

(Edited: 2022-11-02)

Let universe U = {"PersonA", "PersonB", "PersonC", "PersonD"} Knows := {("PersonA", "PersonA"), ("PersonB", "PersonB"), ("PersonC", "PersonC"}, ("PersonD","PersonD")} F := (∀x)Knows(x,x)∧(∃y)¬Knows(z,y)[z -> "PersonB"] T ¬Knows(z,y)[z -> "PersonB", y -> "PersonA"] F T

-- Nov 2 In-Class Exercise Thread

Consider the model M with universe {Tyrell's Secret, Jim's Secret}

Knows := {(Tyrell's Secret,Tyrell's Secret),(Jim's Secret,Jim's Secret)}

M |= (∀x)Knows(x,x)∧(∃y)¬Knows(z,y) [z->Jim's Secret]

M |= (∀x)Knows(x,x)∧(∃y)¬Knows(z,y) [y->Tyrell's Secret, z->Jim's Secret]

(Edited: 2022-11-02)

Consider the model M with universe {Tyrell's Secret, Jim's Secret} Knows := {(Tyrell's Secret,Tyrell's Secret),(Jim's Secret,Jim's Secret)} M |= (∀x)Knows(x,x)∧(∃y)¬Knows(z,y) [z->Jim's Secret] M |= (∀x)Knows(x,x)∧(∃y)¬Knows(z,y) [y->Tyrell's Secret, z->Jim's Secret]

-- Nov 2 In-Class Exercise Thread

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-- Nov 2 In-Class Exercise Thread

Knows(x,y)

U = {A, B}

(∀x)Knows(x,x)[x = (A, A), (B, B)] <=> True

(∃y)¬Knows(z,y)[z = A, y = B] <=> True

(∀x)Knows(x,x)∧(∃y)¬Knows(z,y) <=> True

Knows(x,y) U = {A, B} (∀x)Knows(x,x)[x = (A, A), (B, B)] <=> True (∃y)¬Knows(z,y)[z = A, y = B] <=> True (∀x)Knows(x,x)∧(∃y)¬Knows(z,y) <=> True

-- Nov 2 In-Class Exercise Thread

 (∀x)Knows(x,x) ∧ (∃y)¬Knows(z,y)
 Domain: (Alice, Bob, Cali)
 Knows: (Alice, Alice), (Bob, Bob), (Cali, Cali)
 Right side evaluates to true if we set it's variables to (Bob, Alice) or (Alice, Bob) or (Bob, Cali) or (Alice, Cali) or (Cali, Bob) or (Cali, Alice)

(∀x)Knows(x,x) ∧ (∃y)¬Knows(z,y) Domain: (Alice, Bob, Cali) Knows: (Alice, Alice), (Bob, Bob), (Cali, Cali) Right side evaluates to true if we set it's variables to (Bob, Alice) or (Alice, Bob) or (Bob, Cali) or (Alice, Cali) or (Cali, Bob) or (Cali, Alice)

-- Nov 2 In-Class Exercise Thread

 Predicate: Knows(X, Y)

 Model: M = {“Alice”, “Bob”, “Dave”}
	Knows(“Alice”, “Alice”)
	Knows(“Bob”, “Bob”)
	Knows(“Dave”, “Dave”)

 Formula: (∀x)Knows(x,x)∧(∃y)¬Knows(z,y)

 Variable Assignment: x -> “Dave”, Y -> “Alice”, Z -> “Bob”

(Edited: 2022-11-02)

Predicate: Knows(X, Y) Model: M = {“Alice”, “Bob”, “Dave”} Knows(“Alice”, “Alice”) Knows(“Bob”, “Bob”) Knows(“Dave”, “Dave”) Formula: (∀x)Knows(x,x)∧(∃y)¬Knows(z,y) Variable Assignment: x -> “Dave”, Y -> “Alice”, Z -> “Bob”

-- Nov 2 In-Class Exercise Thread

 (∀x)Knows(x,x) ∧ (∃y)¬Knows(z,y)
 Universe = ["John", "Peter", "Bob"]
 (∀x)Knows(x,x) := {["John", "John"], ["Peter", "Peter"], ["Bob", "Bob"]} = T
 (∃y)¬Knows(z,y) := [z = "John", y = "Peter"] = T 
 (∀x)Knows(x,x) ∧ (∃y)¬Knows(z,y) = T

(∀x)Knows(x,x) ∧ (∃y)¬Knows(z,y) Universe = ["John", "Peter", "Bob"] (∀x)Knows(x,x) := {["John", "John"], ["Peter", "Peter"], ["Bob", "Bob"]} = T (∃y)¬Knows(z,y) := [z = "John", y = "Peter"] = T (∀x)Knows(x,x) ∧ (∃y)¬Knows(z,y) = T