Select the most appropriate statement about each formula. 1: ∀x∀y (x = y → y = x) 2: ∀x (¬(x = x)) 3: ∀x∀y (R(x,y) → ¬R(y,x)) 4: ∃x ∀y R(x,y)匹配题
A
not true in any model
B
true in model with universe {a,b,c} and R = {(a,b), (a,c), (a, a)}
C
true in every model
D
true in model with universe {a,b,c} and R = {(a,b), (b,c), (c,a)}
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[math: ∀x(¬P(x)→Q(x))]
Consider the sentence [math: (∃x(P(x)∧Q(x)))↔((∃xP(x))∧(∃xQ(x)))]. Which of the following is true?(If (D) is true, you must answer (D) and not (B) or (C).)
Select the most appropriate statement about each formula. 1: ∀x (T(x) ∨ ¬T(x)) 2: ∃x∀y (x ≠ y) 3: ∀x∀y (P(x,y) → P(y,x)) 4: ∀x (P(x,x))
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