3.3 De Morgan's Laws

• What are Boolean expressions used to evaluate?

  True or false
• What does the NOT operator do to a condition?

  Negates it
• Match the logical operator with its truth table:

  AND ↔️ | AND | true | false | ||| --- | --- | --- | ||| true | true | false | ||| false | false | false |

  OR ↔️ | OR | true | false | ||| --- | --- | --- | ||| true | true | true | ||| false | true | false |

  NOT ↔️ | NOT | true | false | ||| --- | --- | --- | ||| | false | true |
• What does the AND operator require to evaluate to true?

  Both sides must be true
• What is the result of applying NOT to true?

  False
• What does the AND operator require for an expression to evaluate to true?

  Both sides true
• The NOT operator turns true to false
• De Morgan's Law for AND expressions states that NOT (A AND B) is equivalent to NOT A OR NOT B
• De Morgan's Law for OR expressions states that NOT (A OR B) is equivalent to NOT A AND NOT B
• Boolean expressions are used to evaluate conditions to either true or false
• What does the NOT operator do to a Boolean condition?

  Negates it
• Match the logical operator with its description:

  AND ↔️ Both sides true

  OR ↔️ At least one side true

  NOT ↔️ Negates the condition
• If `A` is `x > 5` and `B` is `y < 10`, then `NOT A OR NOT B` is `(x <= 5) OR (y >= 10)`
• If `A` is `x > 5` and `B` is `y < 10`, then `NOT A AND NOT B` is `(x <= 5) AND (y >= 10)`
• The OR operator requires at least one side to be true.


  True
• The OR operator requires at least one side to be true.


  True
• The OR operator requires at least one side to be true
• Match the Boolean operator with its example and result:

  AND ↔️ `true AND false` → `false`

  OR ↔️ `true OR false` → `true`

  NOT ↔️ `NOT true` → `false`
• The OR operator evaluates to true if at least one side is true.


  True
• Logical operators are used to combine and modify Boolean conditions in expressions
• The OR operator requires both sides of an expression to be true for the entire expression to be true

  False
• Match the logical operator with its function:

  AND ↔️ Requires both sides true

  OR ↔️ Requires at least one side true

  NOT ↔️ Negates the condition
• In De Morgan's Law for AND expressions, if A is true and B is true, then NOT (A AND B) is false

  True
• In De Morgan's Law for OR expressions, if A is true and B is true, then NOT (A OR B) is false


  True
• Order the logical operators from most restrictive to least restrictive based on their truth requirements

  1️⃣ AND

  2️⃣ OR

  3️⃣ NOT
• The AND operator requires both sides of the expression to be true for the entire expression to be true.

  True
• De Morgan's Law for AND expressions simplifies to `NOT (A AND B)` is equivalent to `NOT A OR NOT B`.

  True
• De Morgan's Law for OR expressions simplifies to `NOT (A OR B)` is equivalent to `NOT A AND NOT B`.

  True
• What is the primary benefit of applying De Morgan's Laws to Boolean expressions?

  Improved readability
• The AND operator requires both sides to be true
• The AND operator requires both sides to be true
• What is the requirement for the AND operator to evaluate to true?

  Both sides must be true
• The NOT operator turns true to false and false to true.


  True
• The AND operator evaluates to false if one side is false
• Understanding Boolean expressions is crucial for writing effective code in programming
• In the truth table for AND, the expression 'true AND true' evaluates to true
• Understanding logical operators is crucial for writing effective Boolean expressions in programming


  True
• What is the equivalent expression for NOT (A AND B) according to De Morgan's Law?

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

  NOT A AND NOT B
• The NOT operator changes true to false and false to true


  True