For translating between natural language expressions and logic expressions.
Questions tagged [logic-translation]
542 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
- 869
24
votes
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
- 5,428
13
votes
3 answers
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
- 133
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, $\neg A \lor B$…
bones_mccoy
- 603
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
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
- 2,674
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
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
- 545
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
- 9,440
9
votes
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…
Aemilius
- 3,759
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
6
votes
2 answers
Determining necessary conclusions from logical statements
I am working on a logic problem involving quantified statements, and I need help determining which conclusion necessarily follows.
The premises are:
All lemon cookies are tasty.
Some tasty cookies are expensive.
We need to evaluate which of the…
Nell
- 778
- 5
- 16
6
votes
2 answers
How do I translate "is not sufficient" into symbolic logic?
m
a
m → a
¬(m → a)
T
T
T
F
T
F
F
T
F
T
T
F
F
F
T
F
$m$ := the monkey dances
$a$ := I get an A on the test
$Q$ := the monkey dancing IS SUFFICIENT for me to get an A on the test
$\lnot Q$ := the monkey dancing IS NOT SUFFICIENT for me…
Ben
- 83
6
votes
2 answers
There is an odd number between any two even numbers
Write the complete mathematical logical expression of the following: there is an odd number between any two even numbers.
My attempt:
$E(x): x$ is even.
$O(x): x$ is odd.
$$∀m∀n∃k[(E(m) ∧ E(n) ∧ O(k)) ∧ (m < k < n)]$$
This looks like in English…
Accribus
- 67