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Questions tagged [predicate-logic]

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Extended Boolean Logic

Find the results of the following substitutions. Just give the answer and explain the reasons if the result is undefined: a) (∀𝑥)(𝑓(𝑥) < 7)[𝑥 ≔ 7] b) (∀𝑦)(𝑓(𝑥) < 7)[𝑥 ≔ 7] There is ...
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Negation of the semantics of the Until operator in LTL

I have been looking at the Until operator and the release operator and when introduced to the release operator it was suggested that it is equivalent to: $\phi R \psi \equiv \neg(\neg\phi U \neg \psi)...
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Must $x$ and $y$ be different in a statement of the form $\forall x \forall y \cdots$?

Given the following predicate formula $F$: $$\forall x \forall y [(\text{italian}(x) \Rightarrow (\text{winWC}(y) \Rightarrow \text{happy}(x))]$$ I am having trouble understanding whether $x$ and $y$...
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What does it mean to logically imply another predicate?

Consider the following predicate formulas. $F1: \forall x \exists y ( P(x) \to Q(y) ).$ $F2: \exists x \forall y ( P(x) \to Q(y) ).$ $F3: \forall x P(x) \to \exists y Q(y).$ $F4: \exists x P(x) \...
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predicate logic proof of 2 numbers

For any two different numbers there is an number in between. I'm trying to write this in predicate logic and have no idea how to do it, since I need 2 variables X and Y? For all x there exists a y ...
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predicate logic/binary relation help

(1) ∀x, y, z (x < y ∧ y < z → x < z) (transitivity) (2) ∀x ¬(x < x) (antisymmetry) (3) ∀x, y (x < y ∨ x = y ∨ y < x) (linearity) I need to give an example of a (nonempty) ...
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Discrete Mathematics Proofs for ∃ and ∀

Premises or Givens: $∃x(A(x) → B(x))$ $∀x (B(x) → K(x))$ To Prove: $∃x(A(x) → K(x))$ My Solution: $A(z) → B(z)$ From premise and Existential instantiation $x$ for $z$ $B(z) → K(z)$ From ...