2d3vljtq

Answered

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

I've made 2 translations:

Domain = person in your school

$C(x)=x$ has visited Mexico

$\exists xC(x)$

Domain = people in the world

$S(x)=x$ in your school

$\exists x(S(x)\wedge C(x))$

Yet I don't know what to change to create a third translation.

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

I've made 2 translations:

Domain = person in your school

$C(x)=x$ has visited Mexico

$\exists xC(x)$

Domain = people in the world

$S(x)=x$ in your school

$\exists x(S(x)\wedge C(x))$

Yet I don't know what to change to create a third translation.

Answer & Explanation

vrtuljakc6

Expert

2022-07-16Added 16 answers

Step 1

Domain = all objects

$S(x):=x$ is a person in your school

Step 2

$M(x):=x$ is Mexico

$V(x,y):=x$ has visited y

$\exists x\exists y\phantom{\rule{thickmathspace}{0ex}}{\textstyle (}S(x)\wedge M(y)\wedge V(x,y){\textstyle )}$

Domain = all objects

$S(x):=x$ is a person in your school

Step 2

$M(x):=x$ is Mexico

$V(x,y):=x$ has visited y

$\exists x\exists y\phantom{\rule{thickmathspace}{0ex}}{\textstyle (}S(x)\wedge M(y)\wedge V(x,y){\textstyle )}$

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