1. Which of the following best defines discrete structures?
A. Math that deals with smooth, continuous ranges
B. Math that deals with separate, distinct parts
C. Information measured along an unbroken scale
D. Information represented only by decimals
Explanation: Discrete structures specifically deal with separate and distinct parts rather than continuous ranges.
2. Which of the following represents continuous data?
A. Number of students in a classroom
B. Total count of coins in a jar
C. The exact height or weight of a person
D. Number of chairs in the auditorium
Explanation: Height and weight are measured along an unbroken scale, making them continuous data.
3. What is a mathematical statement that has been proven true beyond any doubt called?
A. A hypothesis
B. A theorem
C. An open sentence
D. A proposition
Explanation: A theorem is defined as a mathematical statement that has been proven true beyond any doubt.
4. Which of the following is considered a valid proposition?
A. Bossing, is that you?
B. Read this carefully.
C. X + 1 = 2
D. Manila is the capital of China.
Explanation: Propositions must be strictly True or False, and 'Manila is the capital of China' is a false proposition.
5. Why is the statement 'X + 1 = 2' NOT a valid proposition?
A. It is phrased as a direct command.
B. It is an interrogative question.
C. It contains an unspecified variable.
D. It is always undeniably true.
Explanation: Open sentences containing unspecified variables do not have a fixed truth value, so they are not propositions.
6. In a valid argument, what happens if all the premises are true?
A. The conclusion is guaranteed to be true.
B. The conclusion might still be false.
C. The argument automatically becomes invalid.
D. The premises cancel each other out.
Explanation: By definition, a valid argument ensures that if all premises are true, the conclusion must also be true.
7. What makes an argument invalid?
A. When the conclusion is always true regardless of premises
B. When the premises are true, but the conclusion might still be false
C. When all premises are proven false
D. When no conclusion is ever stated
Explanation: An argument is invalid if the truth of the premises does not guarantee the truth of the conclusion.
8. What is a compound proposition?
A. A standalone statement with just one idea
B. An unbroken scale of measurement
C. Two or more statements glued together with logical operators
D. A rulebook for digital hardware
Explanation: Compound propositions consist of two or more statements combined using logical operators like AND or OR.
9. What is the rule for a conjunction (p ∧ q)?
A. True only when both p and q are True
B. False only when both p and q are False
C. Inverts the truth value of p
D. True if either p or q is True
Explanation: A conjunction is true only when both constituent statements are true.
10. 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 flips the hypothesis and conclusion to become q → p.
11. What is the contrapositive of the conditional statement p → q?
A. q → p
B. ¬q → ¬p
C. ¬p → ¬q
D. p ∨ q
Explanation: The contrapositive negates both parts and reverses them, resulting in ¬q → ¬p.
12. According to the XOR (Exclusive OR) operation rule, when is P ⊕ Q false?
A. When the values are different
B. When both values are True or both are False ('parehas ang value')
C. Only when P is False and Q is True
D. Only when P is True and Q is False
Explanation: In XOR, if the values are the same ('parehas ang value'), it is automatically false.
13. In a Biconditional operation (P ↔ Q), when is the result false?
A. When both P and Q are True
B. When both P and Q are False
C. When the values are not the same ('hindi parehas ang value')
D. When P is False and Q is True
Explanation: A biconditional yields false if the truth values of P and Q do not match.
14. Under what condition is a Conditional statement (P → Q) evaluated as False?
A. When P is True and Q is False
B. When P is False and Q is True
C. When both P and Q are False
D. When both P and Q are True
Explanation: A conditional statement is only false when the premise (IF) is True and the conclusion (THEN) is False.
15. Which branch of logic specifically analyzes how simple true/false statements combine using connectors?
A. Discrete arithmetic
B. Propositional logic
C. Continuous calculus
D. Empirical geometry
Explanation: Propositional logic is the branch of logic that deals with combining simple true/false statements using logical connectors.