Predicate Logic

∀m[m ∈ R : ∃n[n ∈ N :3m + n> 3]]

For all m in R there is an n in N such that 3m+n is greater than 3

∀m[m ∈ R : ∀n[n ∈ N :3m + n> 3]]

For all m in R and for all n in N it holds that 3m + n is greater than 3

∃m[m ∈ R : ∀n[n ∈ N :3m + n> 3]]

There is an m in R such that for all n in N it holds that 3m + n is greater than 3

∃m[m ∈ R : ∃n[n ∈ N :3m + n> 3]]

There is an m in R and an n in N such that 3m+n is greater than 3

∀n[n ∈ N : ∀m[m ∈ R :3m + n> 3]]

For all natural numbers n and all real numbers m 3m + n > 3

∀n[n ∈ N : ∃m[m ∈ R :3m + n> 3]]

For every natural number n, there exists some real number m such that 3m + n > 3.

∃n[n ∈ N : ∀m[m ∈ R :3m + n> 3]]

There exists a natural number n such that for every real number m, 3m + n > 3

Bound Variable Replacement

Domain Splitting for both quantifiers

One Element Predicates

Empty Domains

Domain Weakening

De Morgan

What is the priority schema for propositional logic