Logical Identities

Which of the following shows De Morgan Law?

• ¬(A ∧ B) = ¬A ∨ ¬B and ¬(A ∨ B) = ¬A ∧ ¬B
• ¬(A ∨ B) = ¬A ∨ B
• ¬(A ∧ B) = A ∨ ¬B
• ¬(A ∨ B) = A ∧ B

Which of the following shows Double Negation Law?

• P = ¬P
• ¬(P ∧ Q) = ¬P ∨ ¬Q
• ¬(¬P) = P
• P ∨ ¬P = Q

Which of the following shows Associative Laws of logic?

• (A ∧ B) ∨ C = A ∧ (B ∨ C)
• (A ∨ B) ∧ C = A ∨ (B ∧ C)
• (A ∧ B) ∧ C = A ∧ (B ∧ C) and (A ∨ B) ∨ C = A ∨ (B ∨ C)
• A ∧ (B ∧ C) = (A ∧ B) ∧ C

Which of the following represents the Idempotent Law?

• A ∧ A = A ∨ A

• A ∨ A = A ∧ A

• A ∨ A = A

• A ∧ A = A

Which of the following illustrates the Absorption Law?

• A ∨ (A ∨ B) = A ∧ B

• A ∧ (A ∨ B) = A

• A ∨ (A ∧ B) = A

• A ∧ (A ∧ B) = A ∨ B

Which of the following demonstrates the Commutative Law?

• A ∨ (B ∧ C) = (A ∨ B) ∧ C

• A ∧ B = B ∧ A

• A ∨ B = A ∧ B

• A ∧ (B ∨ C) = (A ∧ B) ∨ C

Which of the following illustrates the Distributive Law?

• A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)

• A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C)

• A ∧ (B ∨ C) = A ∨ (B ∧ C)

• A ∨ (B ∧ C) = (A ∨ B) ∧ C

Which of the following represents the Negation Law?

• ¬(P ∧ Q) = ¬P ∨ Q

• P ∨ ¬P = True

• ¬(P ∨ Q) = ¬P ∧ Q

• P ∧ ¬P = False

Which of the following demonstrates the Identity Law?

• A ∧ True = A

• A ∨ False = A

• A ∧ False = A

• A ∨ True = A

• ¬q ∨ p
• p ∧ q
• p ↔ q
• ¬p ∨ q