# logic's questions - Chinese 1answer

15.309 logic questions.

### 2 Does there exist an uncountably infinite language?

If an alphabet $= \{a, b\}$ I believe an example of a finite language over that alphabet with positive cardinality would be the set equal to $(a+b)^4$ An example of a countably infinite language ...

### -4 convert into first order logic

0 answers, 13 views logic
Any employee who does not participates for the strike or work in contract basis will report for work. Some employees in contact basis will participate for the meeting. All employees who do the strike ...

### 1 Translation of sentence to logic formula

Here are four sentences: If Jessy moves his truck, Irene will play her guitar Irene will only move her car, if Jessy moves his garbage cans It is not the case, that Jessy will move his ...

### Write the statement in symbolic language

1 answers, 32 views logic
Consider the following statement: One plus the square of an odd natural number is divisible by a product of 2 consecutive natural numbers. Write this in symbolic language. Is it true or false?

### 2 Does the principle of explosion depend on the rules of weakening?

1 answers, 41 views logic

### 2 Why does this theory prove that it's not consistent?

1 answers, 86 views logic proof-theory

### 2 Most adequate logic system to formally prove Euler's identity (and what would the proof look like)?

1 answers, 37 views logic formal-proofs
If we were given the task of proving Euler's identity using a formal logic system, which logic system out there would be the most convenient for such a task? And more or less what would the proof look ...

### 7 Axiom of Regularity allows for this set be an element of itself

3 answers, 244 views logic set-theory
I'm new to set theory, and the axiom of regularity has been giving me some trouble. It states that every non-empty set A has an element B such that A and B are disjoint sets. Apparently, this axiom ...

### 1 On the theorem $(p \cdot q) \supset (p \supset q)$

4 answers, 64 views logic propositional-calculus
In the book Gödel's Proof, by Nagel and Newman, the authors write (p. 119): There is a theorem in logic which reads: $$(p \cdot q) \supset (p \supset q)$$ or when translated, 'If both $p$ ...

### Is it possible to rewrite the solution of an equation as a sequence of logical inferences in a logic system (e.g. FOL, SOL, etc.)?

3 answers, 36 views logic formal-proofs
If I solve an equation, for instance, if I assume the premise 5 * x = 10, I can logically conclude that x = 10 / 5 = 2. This is a trivial example, but even for more complex equations, a correct ...

### 1 Boolean algebra: why does the distributive property not make intuitive mathematical sense?

1 answers, 41 views logic boolean-algebra

### How to symbolize this “only” statement in first-order logic?

I'm having trouble symbolizing this sentence: "Every giraffe loves only Alfred." My thought process was "Every x such that x is a giraffe then it loves something y and y is Alfred." ∀x (Gx → ∃y (L(...

### -4 Gödel's incompleteness theorem doesn't make sense to me [duplicate]

0 answers, 39 views logic
So let's say you have a set of consistent axioms A. GIT states that there are some true statements that cannot be proven from A. But what is truth? Truth is by definition anything that is a logical ...

### -3 Logic programming [on hold]

0 answers, 114 views logic first-order-logic
Any employee who does not participates for the strike or work in contract basis will report for work. Some employees in contact basis will participate for the meeting. All employees who do the strike ...