Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [quantifiers]

The quantifiers $\forall$ ("for all") and $\exists$ ("there exists") distinguish predicate calculus from propositional logic.

Quantifiers specify the quantity of objects that satisfy a given formula.

The quantifiers $\forall$ (for all) and $\exists$ (there exists) are the most common, but others such as $\exists!$ (there exists a unique) are also in usage.

Only use this tag if your question is about the usage of a quantifier in a formula. Be sure not to use this tag for any question with quantifiers.

1826 questions
0
votes
0 answers

Would my answers to this quantifier question also be correct?

Translate these statements into English, where R(x) is “x is a rabbit” and H(x) is “x hops”, and the domain consists of all animals. $$(a) ∀xR(x) → H(x)$$ $$(b) ∀xR(x) ∧ H(x)$$ $$(c) ∃xR(x) → H(x)$$ $$(d) ∃xR(x) ∧ H(x)$$ The answers to these were…
computerscienceisapain
  • 238
0
votes
2 answers

Is $\forall x$ meaningful when there's no (specified or implied) domain for $x$?

Warning: XY problem My recent question here revolved (among other things) on whether the intersection of all elements in an empty set of sets is a matter of definition or convention. When working in a Topological space (X,T), I suggested that for $S…
user019828
  • 83
0
votes
1 answer

I need quick help with quantifiers in this definition below

Given the transition relation $\delta \subseteq S \times \Sigma \times \Gamma \times S$, where the $S$'s are the source and target states respectively, while the $\Sigma$ is the set of input alphabet, and $\Gamma$ is the set of output alphabet. The…
user440526
  • 1
0
votes
1 answer

Proving a quantified statement wrong

The domain is the natural numbers set. I want to prove this statement wrong, however, I'm not sure how should I go about that since, theoretically, I would have to go through all y values in order to find at least one that would be fit for every…
wintersun
  • 13
0
votes
1 answer

Translating plain english to math-ish using quantifiers and modulus

There is a rational number and an irrational number which are 2/3 apart from each other. So far I have : $$\forall \delta >0.\exists x\in\mathbb{Q}. \exists y\in\left(\mathbb{R}/\mathbb{Q}. | x-y| > \frac{2}{3}\delta\right)$$ I'm not too sure on…
omnipotxnce
  • 1
0
votes
1 answer

Compound quantifiers

So basically there's a mathvideo in which there are some examples about compound quantifiers, but of which the answer is not provided. So I have no clue that I'm right or wrong, could someone please check my answers? Thank you in advance. ex.1:…
TheCreator
  • 383
0
votes
1 answer

Quantifiers. Translate english statements into Symbolic Form.

1. All natural numbers are Integer. So I know natural number is N and integer is Z but how do I translate this statement into Symbolic Form ?
user832845
  • 13
0
votes
1 answer

How to understand quantifiers?

"The following statements are about positive real numbers. Which one is true? Explain your answer." $\forall x, \exists y$ such that $xy < y^2$ $\exists x$ such that $\forall y, xy < y^2$ I try understanding this but the English is difficult for…
Pefta Seng
  • 9
0
votes
1 answer

Truth Value of Multiple Quantifiers

I have problem determining truth value of statements involving three quantifiers like this one. $\forall x\ \exists y$ such that $\forall z, x+y = z,$ assuming all variables are real numbers. I normally start these types of problems by trial and…
user74954
  • 1
0
votes
0 answers

Pugh problem 1.3: quantified statements

Recast the following English sentences in mathematics, using correct mathematical grammar. Preserve their meaning. a) $2$ is the smallest prime number. b) The area of any bounded plane region is bisected by some line parallel to the $x$-axis. c)…
John P.
  • 2,136
0
votes
1 answer

Translate into quantified statement

Universe of x: all students Universe of y: all courses A(y): y is an advanced level course F(x): x is a first-year student T(x,y): x is taking y Translate "No first-year student is taking an advanced level course" Is my answer correct: $\forall…
sam
  • 3
0
votes
2 answers

translate the following into quantified statements

M(x) = "x is male" F(x) = "x is female" S(x,y) = "x is scared of y" O(x) = "x is open-minded" Translate the following: a) Some open-minded females fear some closed-minded males. b) No female fears all males. c) Some males are females. d) All males…
sam
  • 3
0
votes
0 answers

Is my quantified statement correct?

Every even integer can be expressed as the sum of two odd integers: This is my try for the statement a=b+c $\small(\forall a{\in}\Bbb Z)(\forall b{\in}Z)(\forall c{\in}\Bbb Z)\big[{[( \exists x{\in}\Bbb Z)(a=2x)\wedge(\exists y{\in}\Bbb…
Manika Sharma
  • 23
0
votes
3 answers

Quantifiers: what's the difference between these formulas?

What differences are there between the following properties: $(\forall j \in \{1,2,3\}) ( \exists a \in \Bbb R) f_j(a)=1$ $ (\exists a \in \Bbb R) (\forall j \in \{1,2,3\}) f_j(a)=1$ $(\exists j \in \{1,2,3\}) ( \forall a \in \Bbb R)…
SAM.Am
  • 387
0
votes
1 answer

Convert the following to clausal form

Convert below into the clausal form: $$\forall\, x\,(\exists\,y\,(q(x)\wedge r(y))\to p(x))$$ I cannot solve this.
Naveen Chalaka
  • 13
1 2 3
4
5 6 7