Boolean Algebra Worksheet

Instructions

Use Java boolean notation: && (AND), || (OR), ! (NOT) Variables: A, B, C, D represent boolean values (true or false)

Part 1: Apply DeMorgan’s Laws

Simplify the following expressions using DeMorgan’s laws:

  1. !(A && B)

  2. !(A || B)

  3. !(A && B && C)

  4. !(!A || B)

  5. !(A || !B) && C

  6. !((A && B) || C)

  7. !(A && (B || C)) || D

  8. !((A || B) && (C || D))

Part 2: Identity Verification

Determine whether each identity is TRUE or FALSE. Show your work using boolean simplification rules:

  1. A && (B || C) = (A && B) || (A && C)

  2. A || (A && B) = A

  3. (A || B) && (A || C) = A || (B && C)

  4. (A || B) && (!A || B) = B

  5. A && (B || C) && (B || !C) = A && B

  6. (A && B) || (A && C) || (!A && B && C) = (A && B) || (A && C)

Part 3: Simplify the Following

Reduce each expression to its simplest form:

  1. A && A

  2. (A || B) && (!A || B)

  3. A && (B || !B)

  4. (A && B) || (A && !B) || (!A && C)

  5. (A || B) && (A || C) && (B || C)

  6. (A && B && C) || (A && B && !C) || (A && !B && C) || (!A && B && C)