Discrete Math (Midterm)

1. Which of the following statement is correct?

P ∨ q ≡ q ∨ p

¬(p ∧ q) ≡ ¬p ∨ ¬q

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

All options are correct

2. P ∨ q is logically equivalent to

¬q → ¬p

Q → p

¬p → ¬q

¬p → q

3. P ↔ q is logically equivalent to

(p → q) → (q → p)

(p → q) ∨ (q → p)

(p → q) ∧ (q → p)

(p ∧ q) → (q ∧ p)

4. (p → q) ∧ (p → r) is logically equivalent to

P → (q ∧ r)

P → (q ∨ r)

P ∧ (q ∨ r)

P ∨ (q ∧ r)

5. P (p ↔ q) is logically equivalent to

Q↔p

P↔¬q

¬p↔¬q

¬q↔¬p

6. P → q is logically equivalent to

¬p ∨ ¬q

P ∨ ¬q

¬p ∨ q

¬p ∧ q

7. P (p ↔ q) is logically equivalent to

P ↔ ¬q

¬p ↔ q

¬p ↔ ¬q

¬q ↔ ¬p

8. P ∧ q is logically equivalent to

¬ (p → ¬q)

(p → ¬q)

(¬p → ¬q)

(¬p → q)

9. (p → r) ∨ (q → r) is logically equivalent to

(p ∧ q) ∨ r

(p ∨ q) → r

(p ∧ q) → r

(p → q) → r