3.4.2 Boolean logic

• Boolean logic often uses the values 0 and 1 or TRUE and FALSE
• What is the mathematical system used to represent truth and falsity in Boolean logic?

  Boolean Logic
• The NOT operator reverses the truth value of the input
• The AND operator returns TRUE if both inputs are TRUE
• What are the three fundamental Boolean operators?

  AND, OR, NOT
• The AND operator returns TRUE if both inputs are TRUE.


  True
• Match the Boolean operator with its symbol:

  AND ↔️ ∧

  OR ↔️ ∨

  NOT ↔️ ¬
• The AND operator returns TRUE if at least one input is TRUE.

  False
• Under what condition does the AND operator return TRUE?

  Both inputs are TRUE
• The OR operator returns TRUE if at least one input is TRUE
• What does the NOT operator do to the truth value of TRUE?

  Changes it to FALSE
• Arrange the Boolean operators in order of their symbols:

  1️⃣ ∧ (AND)

  2️⃣ ∨ (OR)

  3️⃣ ¬ (NOT)
• The OR operator returns FALSE only if both inputs are FALSE.

  True
• What does the NOT operator do to the truth value of FALSE?

  Changes it to TRUE
• The NOT operator returns FALSE if the input is TRUE.

  True
• When does the OR operator return TRUE?

  At least one input is TRUE
• Truth tables show all possible input combinations and corresponding output values.
• What is one application of truth tables in Boolean logic?

  Evaluating Boolean expressions
• What are truth tables used to represent in Boolean logic?

  Boolean logic operations
• Truth tables can determine the final output of a Boolean expression
• How do truth tables help in simplifying Boolean expressions?

  Identify redundant terms
• Two Boolean expressions with the same truth table are logically equivalent.


  True
• Match the Boolean operators with their symbols:

  AND ↔️ ∧

  OR ↔️ ∨

  NOT ↔️ ¬
• A Boolean expression can be either TRUE or FALSE
• Arrange the Boolean operators in order of precedence:

  1️⃣ NOT

  2️⃣ AND

  3️⃣ OR
• What are De Morgan's Laws used for in Boolean algebra?

  Negating Boolean expressions
• Match the operation with its De Morgan's Law:

  NOT (A AND B) ↔️ (NOT A) OR (NOT B)

  NOT (A OR B) ↔️ (NOT A) AND (NOT B)
• De Morgan's Laws are useful for simplifying complex Boolean expressions
• What mathematical system is used to represent truth and falsity in Boolean logic?

  Boolean Logic
• The NOT operator reverses the truth value of the input.

  True
• Under what condition does the AND operator return TRUE?

  Both inputs are TRUE
• The NOT operator is represented by the symbol ¬
• What is a truth table?

  A tabular representation of Boolean logic operations
• Arrange the Boolean operators in order of precedence during evaluation:

  1️⃣ NOT

  2️⃣ AND

  3️⃣ OR
• What determines the final truth value of a Boolean expression?

  Operator precedence
• The negation of (x > 5) AND (y < 10) using De Morgan's Laws is (x ≤ 5) OR (y ≥ 10).


  True
• De Morgan's Laws describe how to negate Boolean expressions involving AND and OR operations.
• What is the equivalent of NOT (A AND B) according to De Morgan's Law?

  (NOT A) OR (NOT B)
• What is the equivalent of NOT (A OR B) according to De Morgan's Law?

  (NOT A) AND (NOT B)
• The negation of (x > 5) AND (y < 10) is (x ≤ 5) OR (y ≥ 10) using De Morgan's Laws.

  True