# Tagged Questions

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### How to express this truth set?

How would you express this truth set in mathematical terms? $4 < x^2 \le 9, X \in \mathbb{R}$
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### Rules of Inference…From the following premises, conclude that p → q.

1. (r ∧ ¬s) ∨ (q ∧ ¬s) 2. ¬s → ((p ∧ r) → u) 3. u → (s ∧ ¬t) ----------------------- Prove from the previous arguments. p → q Hey guys, I am really lost, so far I ...
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### Equivalence Proof (p ∧ q) ∨ ¬(p → q) ∨ ¬(q ∧ r).

I am trying to prove (p ∧ q) ∨ ¬(p → q) ∨ ¬(q ∧ r) ≡ ¬r ∨ (q → p). So far I have done the following: (p ∧ q) ∨ ¬(¬p ∨ q) ∨ ¬(q ∧ r) Implication Definition (p ∧ q) ∨ (p ∧ ¬q) ∨ (¬q ∨ ¬r) De ...
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### Logical implication applied to equation systems

I am interested in mathematical logic, and was wondering if it is common practice / computationally possible to prove if the solution of a set of equations implies all the solutions of another set of ...
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### How to check the validity of this argument using the rules of inference?

I have this argument : I play basketball and football. If today isn't Saturday, then I play basketball and football. If today is Friday OR today is Saturday, then I don't play football. Therefore, ...
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### Convert algebraic formula to CNF

Consider the following test: $$\sum_{i=1}^n{a_ib_ic_i} \overset{?}{=} q,\tag1$$ where $a_i, b_i, c_i \in \{-1, 0, 1\}$ and $q \in \{0, 1\}.$ Is it possible to rewrite [1] to conjunctive normal ...
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### Satisfiability Problem: Determining Which People To Invite

When planning a party you want to know whom to invite. Among the people you would like to invite are three touchy friends. You know that if Jasmine attends, she will become unhappy if Samir is ...
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### Are the following statements TRUE OR FALSE: [closed]

Are the following statements TRUE OR FALSE: [$\forall x \in \mathbb{R}$] [$x > 0$ $\implies$ $x^2 > x$] [$\forall x \in \mathbb{R}$] [$x > 0$] $\implies$ [$\forall x \in \mathbb{R}$] ...
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### Why $\{(f,g) \mid f(0)=g(0)$ or $f(1)=g(1)\}$ is not transitive? [closed]

I'd like to know why $\{(f,g) \mid f(0)=g(0)$ or $f(1)=g(1)\}$ is not transitive ?
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### Defining what a proposition is is in propositional logic

What is an exact definition of a proposition that we can use to apply to sentences in natural language? Are the following propositions? 1.) "I am calling you a liar." 2.) "4 is the square root of ...
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### Why $(a,b)\mid a+b\le3$ is not reflexive and is symmetric?

Why $(a,b)\mid a+b\le3$ is not reflexive and is symmetric? I read because a€ Z so by counter example $(5,5)$, $5+5$ is not less than or equal to $3$ So it's not reflexive But why it's symmetric ? I ...
I'd like to know why the divides relation on the set of positive integers antisymmetric. The book says $a|b$ and $b|a$ then $a=b$. But I think if a|b and b not divides a for example $1|2$ but not ...
### Why $\{(a,b) | a\leq b\}$ is not symmetric?
I want to know why $$\{(a,b) \mid a\leq b\}$$ is not symmetric, when $$\{(a,b) \mid a\leq b\} =\{(a,b)| a<b \text{ or }a=b\}$$ So if a=b that means aRb and bRa so it is symmetric, right ? Thanks ...