Hi everyone,

The review sheet for Exam #2, taking place on Thursday, 10/25, has been posted under `Classroom Resources/Exam Reviews`

. Let me know if you have any questions.

Best,

Prof. Reitz

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Hi everyone,

The review sheet for Exam #2, taking place on Thursday, 10/25, has been posted under `Classroom Resources/Exam Reviews`

. Let me know if you have any questions.

Best,

Prof. Reitz

- Formal proof of a statement involving the interchange of quantifiers October 3, 2024Let $P$ be a formula with two variables. Given the premises: $\forall x \exists y P(x,y)$ $\forall x \forall x' \forall y \forall y' (P(x, y) \land P(x',y') \to y = y')$ I would like to derive $\exists y \forall x P(x,y)$. Informally, the idea is to introduce a function $(f(x) = y) \leftrightarrow P(x,y)$ […]FR09
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- Is $A $ implying $B$ really captured by $A \implies B$? [closed] October 2, 2024Consider for example a common statement for a function f from basic calculus : $$ \text{differentiability of (f)} \implies \text{continuity of (f)} -(1)$$ Now, if we have a function is discontinuous, then it would be an acceptable deduction (... for most math students) to deduce from the above that it can not be differentiable.(*) But, […]Cantor Dust Drachen
- two issues on first order logic's GEN rule [duplicate] October 2, 2024The most popular axiom system for first order logic contains 5 axioms and 2 rules,the rules of inference of any first-order theory are: 1 Modus ponens(MP rule): C follows from B and B → C 2 Generalization(GEN rule): (∀x)B follows from B In the book Introduction to Mathematical Logic (MENDELSON 6th Ed - CRC Press) […]showkey
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- Issue with contrapositive October 1, 2024So contrapositives are logically equivalent statements, which can be useful when proving things. But I'm not convinced that this is true. Take this example: $x \in \mathbb{Z}$. Then $$x \neq 2 \Rightarrow x+1 \neq 0.5$$ is true, but the contrapositive $$x+1 = 0.5 \Rightarrow x=2$$ is false. If one statement is always false/true, then is […]thedanktouch
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- How do I show that $(p \lor q) \land \{\lnot [(\lnot p \land r) \lor q] \}$ is tautology by showing the axiomatic proof? [closed] September 30, 2024I'm getting a bit confused, I was told to answer this but when I try to do it. The expression does not hold true for all truth values of $p,q,$ and $r$. Making $(p \lor q) \land \{\lnot [(\lnot p \land r) \lor q] \}$ not a tautology.Ethaniel Manuel

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