1. What primary characteristic defines discrete structures in mathematics?
A. Smooth, continuous ranges
B. Separate, distinct parts
C. Unbroken scales with decimals
D. Infinite fluctuating curves
Explanation: Discrete structures deal specifically with separate and distinct parts rather than continuous ranges.
2. Which of the following represents an example of continuous data?
A. Number of students
B. Count of coins
C. Total chairs in a room
D. Time taken to run a race
Explanation: Time is measured along an unbroken scale using decimals, making it continuous data.
3. How is a mathematical theorem defined in the document?
A. An untested hypothesis
B. A statement proven true beyond any doubt
C. A command to execute code
D. An open sentence with variables
Explanation: A theorem is explicitly defined as a mathematical statement that has been proven true beyond any doubt.
4. Why is the phrase 'X + 1 = 2' considered not a valid proposition?
A. It is a question
B. It is an imperative command
C. It is an open sentence with an unspecified variable
D. It is always strictly false
Explanation: Open sentences containing unspecified variables lack a definitive true or false value until the variable is known.
5. What is the truth value of the valid proposition 'Manila is the capital of China'?
A. True
B. False
C. Neither True nor False
D. Both True and False
Explanation: Manila is the capital of the Philippines, making the statement false.
6. What defines a valid argument in logic?
A. The conclusion is always false
B. If all premises are true, the conclusion is guaranteed to be true
C. The premises can be true while the conclusion is false
D. It contains no propositions
Explanation: A valid argument guarantees that a true set of premises forces the conclusion to be true.
7. In the invalid argument example about rain and wet ground, why is the conclusion considered invalid?
A. Because rain never makes the ground wet
B. Because the ground could be wet from another source like watering a garden
C. Because the premises are both false
D. Because the conclusion contradicts the premises
Explanation: The ground being wet does not exclusively mean it rained, as alternative sources like a garden hose could cause it.
8. What is the main function of propositional logic?
A. Measuring continuous physical variables
B. Analyzing how simple true/false statements combine using connectors
C. Solving calculus differential equations
D. Generating random numerical data
Explanation: Propositional logic analyzes the combination of simple true/false statements via logical operators.
9. Which term describes a statement formed by combining two or more ideas with logical operators?
A. Single proposition
B. Compound proposition
C. Discrete structure
D. Continuous data
Explanation: A compound proposition consists of two or more statements glued together using logical operators.
10. When is a conjunction (p ∧ q) considered true?
A. When at least one proposition is true
B. When both propositions are false
C. When both propositions are true
D. When p is false and q is true
Explanation: A conjunction is true only when both constituent propositions are true.
11. What is the rule for a disjunction (p ∨ q) being false?
A. It is false only when both are false
B. It is false when both are true
C. It is always false
D. It is false when p is true
Explanation: A disjunction evaluates to false exclusively when both component statements are false.
12. Given a conditional statement p → q, what is its converse?
A. ¬p → ¬q
B. ¬q → ¬p
C. q → p
D. p ∧ q
Explanation: The converse of a conditional statement p → q simply flips the positions to become q → p.
13. What is the inverse of the conditional statement p → q?
A. ¬p → ¬q
B. q → p
C. ¬q → ¬p
D. p ∨ ¬q
Explanation: The inverse negates both components of the original conditional statement, resulting in ¬p → ¬q.
14. Which of the following correctly defines the contrapositive of p → q?
A. q → p
B. ¬p → ¬q
C. ¬q → ¬p
D. p ↔ q
Explanation: The contrapositive flips and negates both parts of the conditional statement to form ¬q → ¬p.
15. According to the XOR rule (P ⊕ Q), what is the outcome when both P and Q are True (T)?
A. True
B. False
C. Neither
D. Depends on R
Explanation: For XOR, if the values are matching ('parehas ang value'), the result is automatically false.
16. Under the Biconditional rule (P ↔ Q), what happens when P is True and Q is False?
A. The result is True
B. The result is False
C. The result depends on XOR
D. The result is undefined
Explanation: For biconditional statements, if the values are not matching ('hindi parehas ang value'), the result is automatically false.
17. In a Conditional statement (P → Q), under what exact condition is the outcome False?
A. When both P and Q are False
B. When P is True and Q is False
C. When P is False and Q is True
D. When both P and Q are True
Explanation: A conditional statement is only false when the 'IF' statement is True and the 'THEN' statement is False.
18. In the comprehensive truth table provided, what is the value of R when P is True, Q is True, and the third row is evaluated?
A. True
B. False
C. Null
D. Undefined
Explanation: In the third row of the truth table, the R column value listed is True.
19. What is the final evaluated result of the complex expression [(P∧¬Q)∨(R⊕Q)]↔[P→(Q∨R)] in the very first row of the table?
A. True
B. False
C. Both
D. Inconclusive
Explanation: The final column of the truth table shows that the first row evaluates to False.
20. How many rows of T/F combinations are evaluated in the multi-variable truth table provided at the end of Lesson 2?
A. 4 rows
B. 6 rows
C. 8 rows
D. 16 rows
Explanation: The table maps out 8 rows representing all possible combinations for three variables (P, Q, R).