2d3vljtq

2022-07-15

Creating equivalent expressions by changing the domains and predicates
I'm having trouble finding a third way to make a logical expression.
Translate this statement into a logical expression in 3 different ways by varying the domain and by using predicates with one and with two variables.
Someone in your school has visited Mexico
Domain = person in your school
$C\left(x\right)=x$ has visited Mexico
$\exists xC\left(x\right)$
Domain = people in the world
$S\left(x\right)=x$ in your school
$\exists x\left(S\left(x\right)\wedge C\left(x\right)\right)$
Yet I don't know what to change to create a third translation.

vrtuljakc6

Expert

Step 1
Domain = all objects
$S\left(x\right):=x$ is a person in your school
Step 2
$M\left(x\right):=x$ is Mexico
$V\left(x,y\right):=x$ has visited y
$\exists x\exists y\phantom{\rule{thickmathspace}{0ex}}\left(S\left(x\right)\wedge M\left(y\right)\wedge V\left(x,y\right)\right)$

Do you have a similar question?