| Universal Argument Forms from Section 3.4 | |
|---|---|
| Universal Instantiation | ∀ x ∈ S ( P(x) )
y ∈ S ∴ P(y) |
| Universal Modus Ponens | ∀ x ∈ S ( P(x) → Q(x) )
y ∈ S ∧ P(y) ∴ Q(y) |
| Universal Modus Tollens | ∀ x ∈ S ( P(x) → Q(x) )
y ∈ S ∧ ~Q(y) ∴ ~P(y) |
| Universal Transitivity | ∀ x ∈ S ( P(x) → Q(x) )
∀ x ∈ S ( Q(x) → R(x) ) ∴ ∀ x ∈ S ( P(x) → R(x) ) |
| Invalid Universal Argument Forms | |
| Universal Converse Error | ∀ x ∈ S ( P(x) → Q(x) )
y ∈ S ∧ Q(y) ∴ P(y) (invalid conclusion!!) |
| Universal Inverse Error | ∀ x ∈ S ( P(x) → Q(x) )
y ∈ S ∧ ~P(y) ∴ ~Q(y) (invalid conclusion!!) |