Discrete Math (Midterm)

9 Questions | Total Attempts: 283

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• 1.
P → q is logically equivalent to
• A.

¬p ∨ ¬q

• B.

P ∨ ¬q

• C.

¬p ∨ q

• D.

¬p ∧ q

• 2.
P ∨ q is logically equivalent to
• A.

¬q → ¬p

• B.

Q → p

• C.

¬p → ¬q

• D.

¬p → q

• 3.
¬ (p ↔ q) is logically equivalent to
• A.

Q↔p

• B.

P↔¬q

• C.

¬p↔¬q

• D.

¬q↔¬p

• 4.
P ∧ q is logically equivalent to
• A.

¬ (p → ¬q)

• B.

(p → ¬q)

• C.

(¬p → ¬q)

• D.

(¬p → q)

• 5.
Which of the following statement is correct?
• A.

P ∨ q ≡ q ∨ p

• B.

¬(p ∧ q) ≡ ¬p ∨ ¬q

• C.

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

• D.

All options are correct

• 6.
P ↔ q is logically equivalent to
• A.

(p → q) → (q → p)

• B.

(p → q) ∨ (q → p)

• C.

(p → q) ∧ (q → p)

• D.

(p ∧ q) → (q ∧ p)

• 7.
(p → q) ∧ (p → r) is logically equivalent to
• A.

P → (q ∧ r)

• B.

P → (q ∨ r)

• C.

P ∧ (q ∨ r)

• D.

P ∨ (q ∧ r)

• 8.
(p → r) ∨ (q → r) is logically equivalent to
• A.

(p ∧ q) ∨ r

• B.

(p ∨ q) → r

• C.

(p ∧ q) → r

• D.

(p → q) → r

• 9.
¬ (p ↔ q) is logically equivalent to
• A.

P ↔ ¬q

• B.

¬p ↔ q

• C.

¬p ↔ ¬q

• D.

¬q ↔ ¬p