For translating between natural language expressions and logic expressions.
Questions tagged [logic-translation]
556 questions
37
votes
4 answers
Difference between "for any" and "for all"?
Though searching for previous questions returns thousands of results for the query "for any" "for all" , none specifically address the following query: I'm reading a textbook in which one definition requires that some condition holds for any $x,\ x'…
Bernd
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24
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3 answers
Does "either" make an exclusive "or"?
When I mean the standard, inclusive "or", I avoid pairing it with "either", because to me this makes "or" feel like the exclusive "or". However, in the language of logic and proofs, does the phrasing "either A or B" mean "A or B, but not both"?
Jonathan Hebert
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The meaning of an implication with the existential quantifier
My professor answered my question on a class discussion board for Discrete Math, but it seems that his answer is just not correct. Could another person who is familiar with this topic weigh in? For context, the function $C(x)$ means that $x$ is a…
Edward45
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12
votes
7 answers
Why is "A only if B" equivalent to "(not A) or B"?
I've encountered this recently and I just can't wrap my head around it. My book states that $$A \rightarrow B \equiv \neg A \lor B$$ It's my understanding that $A \rightarrow B$ means that if $A$ is true, then $B$ is true. But, $\neg A \lor B$ would…
bones_mccoy
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11
votes
3 answers
Difference between “for some $k$” and “for some arbitrary $k$”
I am told that the “for some” and “for some arbitrary” are different. For example, when proving the statement “if n is odd, then $n^2$ is odd”, one of the steps includes writing $$\text{$n = 2k+1,\:\:$ where $k$ is some integer}.$$ I am told that…
bluesky
- 225
11
votes
2 answers
Is it a convention that the word "where" following a mathematical formula needs a comma before it?
I am not a native english speaker. I learnt about defining and non-defining relative clauses from english grammar books. Grammar books tell me not to use commas in defining relative clauses, so I don't understand why there is a comma preceding…
lightweight
- 317
10
votes
1 answer
Is this correctly worded? "If there exist integers $m$ and $n$ such that $12m + 15n = 1$, then $m$ and $n$ are both positive."
In "A Transition to Advanced Mathematics", 8th edition, by Smith, Eggen and St. Andre, exercise 1(f) in chapter 1.6 on page 60 says: Prove that if there exist integers $m$ and $n$ such that $12m + 15n = 1,$ then $m$ and $n$ are both positive. This…
Ben
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10
votes
2 answers
How to convert numerical claims to first order logic?
A). There are atmost 2 apples ? B). There are exactly 2 apples ? C). There is atmost 1 apple ? D). There is exactly 1 apple ? Is there any procedure to convert these type of english sentences as generally we have "For All" and "There Exists" in the…
Jon Garrick
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9
votes
5 answers
Is "William only eats icecream when the sun is shining" a biimplication?
William only eats icecream when the sun is shining Let $P(t)$ be the sun is shining at time $t.$ Let $Q(t)$ be William is eating an icecream at time $t.$ Which implication is there between $P(t)$ and $Q(t)?$ My friend has suggested that it is a…
9
votes
2 answers
What are the rules for the use of dots rather than parentheses in logical formulae?
What are the rules of omission of parentheses of formulas in mathematical logic ? in my text , first order logic mathematical logic by angelo margaris ed 1990 dover , the paretheses is omitted for example in page 49 , $S$ $\rightarrow$ $.$ $P$…
FNH
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9
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3 answers
Writing predicates - is the quantifier necessary?
I'm taking a course in mathematical logic, it has recently covered quantifiers and now I find myself somewhat confused whether or not the existential quantifier is necessary - consider this example: Disclaimer: Assume that our universe is the set of…
Aemilius
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8
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3 answers
How to formalise “There are two students who between them have chatted with everyone else”?
From Discrete Mathematics and Its Applications by Kenneth H. Rosen, 8th edition : Let $C(x, y)$ be the predicate “ $x$ has chatted with $y$ ”, where the domain for $x$ and $y$ consists of all the students in the class. Translate the following…
Saaqib Mahmood
- 27,852
8
votes
2 answers
A negation producing mathematical nonsense?
The mathematical statement $\exists h{\in} \mathbb{R} \quad \dfrac{1}{h}=5\tag*{}$ seems a mathematical statement that is true. However, its negation $\forall h{\in} \mathbb{R} \quad \dfrac{1}{h}\neq 5\tag*{}$ is not a mathematical statement,…
boyler
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8
votes
3 answers
When to use which quantifier with predicate logic?
I'm following my first logic course as part of my pre-masters programme. Currently I'm working on predicate logic. I know that $∀$ is the universal quantifier, which stands for "all" or "every", and $∃$ is the existential quantifier, which stands…
Bart
- 83
7
votes
3 answers
The use of the word "precisely" in mathematical statements
I am having trouble with the word precisely in this sentence and generally, probably, in any mathematical context. A statement reads The points within the parallelpiped determined by $\boldsymbol{a}$ , $\boldsymbol{b}$ , and $\boldsymbol{c}$ are…
AndJM
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