P310 Valid Reasoning II

Professor: Craig DeLancey

Office: Marano 212A

Email: craig.delancey@oswego.edu

**Current Assignments**

**Tentative assignments**

**25 February**
Just a reminder that my textbook
covers quickly the quantified logic in chapters 11-16. Chapter 17
also has some of the material that we will be covering.

**Prove:**
- Using any of our tools, prove:
(A ⊆ B ↔ A ∩ B = A)

Hint: it is sufficient to prove:

(∀x(x ∈ A → x ∈ B) ↔ ∀x((x ∈ A ^ x ∈ B) ↔ x ∈ A))
- Using any of our tools, prove:
(A ⊆ B ↔ A ∪ B = B)

Hint: it is sufficient to prove:

(∀x(x ∈ A → x ∈ B) ↔ ∀x((x ∈ A v x ∈ B) ↔ x ∈ B))
- We can define "-" in the following way:
∀x(x ∈ A - B ↔ (x ∈ A ^ ¬ x ∈ B)).

Using any of our tools, prove:
(A ⊆ B ↔ A - B = {})

Hint: it is sufficient to prove:

(∀x(x ∈ A → x ∈ B) ↔ ¬∃x(x ∈ A ^ ¬ x ∈ B))

**13 May**
Final exam in our classroom 10:30-12:30. Logic approved pop-tarts
will be provided!