/sci/ - Science & Math

>>14886229
>>14886229
Define [eqn] D(x) \Longleftrightarrow x \text{ is a dog} \\ C(x) \Longleftrightarrow x \text{ is a dog} \\ xLy \Longleftrightarrow x \text{ likes } y [/eqn]

Logic is really just symbolic manipulations, language can sometimes be confusing. Intuitively "No dog likes any cat" means "All dogs dislike all cats".
Which can be represented as [math] \forall x \forall y : \left[ D(x) \wedge C(y) \right] \longrightarrow \neg (xLy) [/math] which you can prove is equivalent to [math] \neg \exists x \exists y : D(x) \wedge C(y) \wedge xLy [/math]

If you're still confused then think about the difference between these two statements
"No one can kill anyone" (this proposition is false because there exists at least one person who killed at least one person)
"No one can kill everyone" (this proposition is true because we would all be dead)