Boolean expressions and simplification

• What is a Boolean expression?

  A statement that evaluates to true or false
• When is the expression `a AND b` true?

  When both a and b are true
• What do Boolean expressions use to represent conditions?

  Boolean variables and logical operators
• What is the result of the expression `x > 5` if x is 7?

  True
• How does the truth table help in understanding Boolean expressions?

  It shows results for all variable combinations
• What does the NOT operator do in Boolean logic?

  It inverts the truth value of a variable
• What does the NOT operator do to a variable?

  Inverts the value of a variable
• What is the truth table for the OR operator?

  • True OR True = True
  • True OR False = True
  • False OR True = True
  • False OR False = False
• What does the expression `c OR d` evaluate to if c is false and d is true?

  True
• What condition must be met for the OR operator to return true?

  At least one variable must be true
• What does the truth table for `x AND (y OR NOT x)` illustrate?

  • Shows combined use of operators
  • Displays results for all variable combinations
  • Helps understand logical relationships
• What is the result of `NOT x` when `x` is false?

  True
• What is the truth table for the AND operator?

  • True AND True = True
  • True AND False = False
  • False AND True = False
  • False AND False = False
• What is the output of `x AND (y OR NOT x)` when `x` is False and `y` is False?


  False
• What is the output of `x AND (y OR NOT x)` when `x` is False and `y` is True?

  False
• In the expression `x AND y`, when is the result true?

  When both `x` and `y` are true
• What is the output when the sensor inputs are 0 0 1?


  0
• What is the output of `x AND (y OR NOT x)` when `x` is True and `y` is False?

  False
• What is the output of `x AND (y OR NOT x)` when `x` is True and `y` is True?

  True
• When is the expression `x OR y` true?

  If either `x` or `y` is true
• How do Boolean operators assist in programming and digital circuits?

  They build logical conditions for operations
• What are the main operators used in Boolean expressions?

  AND, OR, and NOT
• What is the output when the sensor inputs are 1 0 1?


  1
• What is the output when the sensor inputs are 1 1 1?

  0
• What is the output when the sensor inputs are 1 0 0?


  0
• What are the four possible output states based on the sensor inputs?

  • Output = 0 (close valve)
  • Output = 0 (sensors agree)
  • Output = 1 (open valve)
  • Output = 1 (sensors disagree)
• What is the output when the sensor inputs are 1 1 0?


  1
• What is the output when the sensor inputs are 0 0 0?


  0
• What is the result of $x OR x$ according to the Idempotent Law?


  $x$
• What are the two possible sensor input states?

  • Good Flame
  • Sensor Disagreement
• What does a truth table show?

  Output for all possible input combinations
• How does a truth table help in Boolean expression evaluation?

  It illustrates how logical operators work together
• What are the key factors that determine the output based on the sensor inputs?

  • Whether the sensor inputs agree or disagree
  • Whether the sensor inputs indicate a good flame or sensor disagreement
• What is the purpose of Boolean algebra rules?

  To simplify expressions
• Why does `x AND (y OR x)` simplify to `x`?

  Because it is true when `x` is true
• How can you rearrange $(x OR y) OR z$ using the Associative Property?


  $x OR (y OR z)$
• What is the Distributive Property in Boolean algebra?

  • $a AND (b OR c) =$$(a AND b) OR (a AND c)$
  • Example: $x AND (y OR x) =$$x$
• What does the Complement Law state in Boolean algebra?

  • $a AND NOT a =$$0$
  • $a OR NOT a =$$1$
  • Example: $x AND NOT x =$$0$
• How do Boolean algebra rules affect expression complexity?

  They reduce expression complexity
• What is the Associative Property in Boolean algebra?

  • $(a AND b) AND c =$$a AND (b AND c)$
  • $(a OR b) OR c =$$a OR (b OR c)$
  • Example: $(x OR y) OR z =$$x OR (y OR z)$