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What is the construct or theory behind the rule concerning the direct proof of a universal statement

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Propositional Logic with Two Statements

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Nested Quantification of exactly one.

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How to read predicate formulas

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Use logic quantifiers to write...

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(P and(not(not P or Q))) or( P and Q) equals P

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Help with logical quantifiers

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How would I translate this sentence into a predicate formula

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40
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If all men were good, there would be no wars

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Existance of an (in)finite theory having infinite model

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233
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Why is this predicate false?

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Structural induction proof

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Translate the following into predicate calculus. State assumed universe of discourse

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Determine whether or not $∀x[p(x) → q(x)]$ and $[∀xp(x)] → [∀xq(x)]$ are logically equivalent.

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The scope of quantifiers

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