/sci/ - Science & Math

[Anonymous No.5223846]

New to predicate logic, have a question.
I want to formalize this into a sentence:
Bulma cannot outrun any man on the team.
My answer is:
∀x.(Man(x) ⇒¬Outrun(x))
Is this okay or do I need to specifically mention Bulma.

[Anonymous No.5223853]

After further thought I have changed my answer to∀x.(Man(x) ⇒¬Outrun(b,x))
outrun(b,x) meaning bulma outrunning x

[Anonymous No.5223857]

Let's say : outrun(x,y) means x outrun y
man(x) : x is a man
bulma : is a constance that identify bulma
your sentence would be :
∀x(man(x) => ¬outrun(bulma, x))

[Anonymous No.5223858]

>∀x
any man, and "any man on a team" is quite different

[Anonymous No.5223879]

>>5223857
Thank you for confirming I can try and tackle the rest of the problems now.

>>5223858
I can just have the universe of discourse as people on the team right

[Anonymous No.5223956]

>>5223879
yes, you can always introduce new quantifier which rain over a subset <span class="math">S={x:\chi_S(x)}[/spoiler] of a domain <span class="math">D[/spoiler], given by a characteristic function <span class="math">\chi_S[/spoiler] (yes/no function/predicate specifying the subset) in the following way:

<span class="math">\forall_S x(P(x)):=\forall_D x(\chi_S(x)\implies P(x))[/spoiler]

[Anonymous No.5223959]

>>5223879
yes, you can always introduce new quantifier which rain over a subset <span class="math">S={x:\chi_S(x)}[/spoiler] of a domain <span class="math">D[/spoiler], given by a characteristic function <span class="math">\chi_S[/spoiler] (yes/no function/predicate specifying the subset) in the following way:

<span class="math">\forall_S x(P(x)):=\forall_D x(\chi_S(x)\rightarrow P(x))[/spoiler]