Boolean Expressions - AP Computer Science Principles

1. What is the result of the Boolean expression: $\text{NOT } (true \text{ AND } true)$?

   false. Parentheses evaluate first: $(true \text{ AND } true) = true$, then $\text{NOT } true = false$.

2. Identify the result: $\text{NOT } (false \text{ AND } true)$

   true. Parentheses evaluate first: $(false \text{ AND } true) = false$, then $\text{NOT } false = true$.

3. What is the result of the expression: $\text{NOT } (true \text{ OR } false)$?

   false. Parentheses force OR first, then NOT: $\text{NOT } true = false$.

4. What is the result of the expression: $true \text{ AND } (\text{NOT } false)$?

   true. $\text{NOT } false = true$, then $true \text{ AND } true = true$.

5. What does the Boolean expression $x \text{ AND } y$ evaluate if $x = false$?

   false. AND returns false when either operand is false.

6. What is the result of the expression: $\text{NOT } (false \text{ OR } true)$?

   false. Parentheses evaluate first: $(false \text{ OR } true) = true$, then $\text{NOT } true = false$.

7. State De Morgan's Law for NOT (A AND B).

   NOT A OR NOT B. De Morgan's Law distributes NOT over AND.

8. State De Morgan's Law for NOT (A OR B).

   NOT A AND NOT B. De Morgan's Law distributes NOT over OR.

9. Identify the result: $false \text{ AND } (true \text{ OR } false)$

   false. Parentheses evaluate first: $(true \text{ OR } false) = true$, then $false \text{ AND } true = false$.

10. What is the result of the expression: $(true \text{ AND } false) \text{ OR } false$?

    false. Parentheses evaluate first: $(true \text{ AND } false) = false$, then $false \text{ OR } false = false$.

11. What is the result of the Boolean expression: $\text{NOT } (true \text{ OR } true)$?

    false. Parentheses evaluate first: $(true \text{ OR } true) = true$, then $\text{NOT } true = false$.

12. What is the result of $true \text{ OR } (\text{NOT } true)$?

    true. $\text{NOT } true = false$, then $true \text{ OR } false = true$.

13. Which Boolean operator is associative: AND, OR, NOT?

    AND, OR. Both AND and OR can group operands differently without changing result.

14. What is the result of the expression: $\text{NOT } (true \text{ AND } false)$?

    true. Parentheses evaluate first: $(true \text{ AND } false) = false$, then $\text{NOT } false = true$.

15. What is the precedence order of Boolean operators NOT, AND, OR?

    NOT, AND, OR. NOT has highest precedence, then AND, then OR.

16. What is the result of the expression: $\text{NOT } (false \text{ OR } false)$?

    true. Parentheses evaluate first: $(false \text{ OR } false) = false$, then $\text{NOT } false = true$.

17. What is the identity element for the AND operation?

    true. AND with true leaves the other operand unchanged.

18. What does the expression $x \text{ AND } x$ simplify to?

    x. Idempotent law: a variable AND with itself equals itself.

19. What is the result of $false \text{ OR } (\text{NOT } false)$?

    true. $\text{NOT } false = true$, then $false \text{ OR } true = true$.

20. What is the result of the expression: $true \text{ OR } (false \text{ AND } true)$?

    true. Parentheses evaluate first: $(false \text{ AND } true) = false$, then $true \text{ OR } false = true$.

21. What is the result of the Boolean expression: $\text{NOT } false$?

    true. NOT reverses the Boolean value.

22. What is the result of the Boolean expression: $\text{NOT } true$?

    false. NOT reverses the Boolean value.

23. Which Boolean operation is performed first: AND or OR?

    AND. AND has higher precedence than OR in Boolean operations.

24. What does the expression $x \text{ OR } \text{NOT } x$ simplify to?

    true. Complement law: a variable OR its negation always equals true.

25. Which Boolean operator is commutative: AND, OR, NOT?

    AND, OR. Both AND and OR can switch operand order without changing result.

26. What is the result of the Boolean expression: $true \text{ AND } true$?

    true. AND returns true only when both operands are true.

27. What is the result of the Boolean expression: $(\text{NOT } false) \text{ AND } true$?

    true. Parentheses evaluate first: $(\text{NOT } false) = true$, then $true \text{ AND } true = true$.

28. What is the result of the expression: $true \text{ AND } false \text{ OR } true$?

    true. AND evaluates first: $(true \text{ AND } false) \text{ OR } true = false \text{ OR } true = true$.

29. What is the result of the Boolean expression: $(\text{NOT } true) \text{ OR } false$?

    false. Parentheses evaluate first: $(\text{NOT } true) = false$, then $false \text{ OR } false = false$.

30. What does the expression $x \text{ AND } \text{NOT } x$ simplify to?

    false. Complement law: a variable AND its negation always equals false.

31. What is the identity element for the OR operation?

    false. OR with false leaves the other operand unchanged.

32. What does the Boolean expression $x \text{ OR } y$ evaluate if $x = true$?

    true. OR returns true when either operand is true.

33. What is the result of the Boolean expression: $\text{NOT } (\text{NOT } false)$?

    false. Double negation: $\text{NOT } (\text{NOT } false) = \text{NOT } true = false$.

34. What is the result of the Boolean expression: $true \text{ OR } false$?

    true. OR returns true if at least one operand is true.

35. What is the result of $false \text{ AND } (\text{NOT } true)$?

    false. $\text{NOT } true = false$, then $false \text{ AND } false = false$.

36. What is the result of the Boolean expression: $true \text{ AND } (\text{NOT } false)$?

    true. $\text{NOT } false = true$, then $true \text{ AND } true = true$.

37. What is the result of the Boolean expression: $(\text{NOT } true) \text{ AND } false$?

    false. Parentheses evaluate first: $(\text{NOT } true) = false$, then $false \text{ AND } false = false$.

38. What does the expression $x \text{ OR } x$ simplify to?

    x. Idempotent law: a variable OR with itself equals itself.

39. What is the result of the Boolean expression: $false \text{ OR } false$?

    false. OR returns false only when both operands are false.

40. What is the result of the Boolean expression: $true \text{ AND } false$?

    false. AND requires both operands to be true.

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