Boolean Algebra

• What is the commutative law for AND in Boolean algebra?

  A.B = B.A
• What is the commutative law for OR in Boolean algebra?

  A + B = B + A
• What is the commutative law for XOR in Boolean algebra?

  A⊕B = B⊕A
• What is the associative law for AND in Boolean algebra?

  A.(B.C) = (A.B).C
• What is the associative law for OR in Boolean algebra?

  A + (B + C) = (A + B) + C
• What is the associative law for XOR in Boolean algebra?

  A ⊕ (B⊕C) = (A⊕B) ⊕ C
• What is the purpose of the distributive law in Boolean algebra?

  To expand brackets in expressions
• What is the distributive law in Boolean algebra?

  A.(B + C) = A.B + A.C
• How can you factorise expressions in Boolean algebra?

  By identifying common factors in terms
• What does the OR operation output when both inputs are true?


  1 (true)
• What does the AND operation output when both inputs are true?

  1 (true)
• What does the NOT operation output?

  The opposite value of the input
• What does the XOR operation output when both inputs are true?

  0 (false)
• How do you simplify the expression P.(0 + P)?

  1. Apply distributive law: P.(0 + P) = P.0 + P.P
  2. Use annulment law: P.0 = 0
  3. Use idempotent law: P.P = P
  4. Final result: P
• How do you simplify the expression Q.(Q + P) + P.(Q + P)?

  1. Expand brackets: Q.Q + Q.P + P.Q + P.P
  2. Use idempotent law: Q + Q.P + P.Q + P
  3. Factorise: Q(1 + P) + P(Q + 1)
  4. Use annulment law: Q + P
• What does the absorptive law state in Boolean algebra?

  A + (A.B) = A
• What is the order of precedence in Boolean algebra?

  Brackets, NOT, XOR, AND, OR
• How is TRUE represented in Boolean algebra?

  By 1
• How is FALSE represented in Boolean algebra?

  By 0
• What does the logical operator OR represent in Boolean algebra?

  A + B represents A OR B
• What does the logical operator AND represent in Boolean algebra?

  A.B represents A AND B
• What does the logical operator NOT represent in Boolean algebra?

  Ā represents NOT A
• What does the logical operator XOR represent in Boolean algebra?

  A⊕B represents A XOR B
• What are the laws for simplifying Boolean expressions using OR operation?

  • Identity law: A + 0 = A
  • Annulment law: A + 1 = 1
  • Idempotent law: A + A = A
  • Inverse law: A + Ā = 1
• What are the laws for simplifying Boolean expressions using AND operation?

  • Identity law: A.1 = A
  • Annulment law: A.0 = 0
  • Idempotent law: A.A = A
  • Complement law: A.Ā = 0