MAT114 COMPLETE STUDY GUIDE
2025/2026 – VERIFIED EXAM QUESTIONS
AND CORRECT SOLUTIONS WITH
RATIONALES
|| 100% GUARANTEED PASS
<LATEST VERSION>
Part 1: Set Theory & Logic
1. What is the set of all elements that are in set A or in set B or in both?
A) Intersection
B) Union
C) Complement
D) Subset
Rationale: The union of two sets, denoted A ∪ B, is defined as the set containing
all elements that are in A, or in B, or in both.
2. In a group of 50 people, 30 like coffee, and 20 like tea. If 10 like both, how
many like neither?
A) 0
B) 10
C) 20
D) 40
Rationale: Using the principle of inclusion-exclusion: |C ∪ T| = |C| + |T| - |C ∩ T|
= 30 + 20 - 10 = 40. So, 40 people like at least one drink. Therefore, 50 - 40 = 10
like neither.
3. The statement "If it is raining, then the ground is wet" is given. What is its
contrapositive?
A) If the ground is not wet, then it is not raining.
,B) If the ground is wet, then it is raining.
C) If it is not raining, then the ground is not wet.
D) It is raining and the ground is wet.
Rationale: The contrapositive of "If P, then Q" is "If not Q, then not P." It is
logically equivalent to the original statement.
4. What is the truth value of the statement: "5 > 3 AND 2 + 2 = 5"?
A) True
B) False
C) Cannot be determined
Rationale: A logical "AND" is true only if both parts are true. Since 2 + 2 = 5 is
false, the entire compound statement is false.
5. If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∩ B?
A) {1, 2, 3, 4, 5}
B) {3}
C) {1, 2}
D) { }
Rationale: The intersection (∩) is the set of elements common to both A and B.
The only common element is 3.
6. The set of all possible outcomes of an experiment is called the:
A) Event
B) Sample Space
C) Union
D) Probability Set
Rationale: By definition, the sample space is the set of all possible outcomes.
7. Which logical operator is represented by the symbol "∨"?
A) And
B) Or
C) Not
D) Implies
Rationale: In logic, "∨" is the symbol for disjunction, meaning "or".
, 8. What is the complement of set A?
A) All elements not in A, within a given universal set.
B) All elements in A.
C) The union of A with itself.
D) The intersection of A with another set.
Rationale: The complement of A, often denoted Aᶜ or A', consists of all elements
in the universal set that are not in A.
9. A truth table for a compound statement with 2 simple statements (P, Q) has
how many rows?
A) 2
B) 3
C) 4
D) 8
Rationale: The number of rows in a truth table is 2ⁿ, where n is the number of
simple statements. 2² = 4.
10. De Morgan's Law states that the complement of (A ∪ B) is equivalent to:
A) Aᶜ ∪ Bᶜ
B) A ∩ B
C) Aᶜ ∩ Bᶜ
D) A ∪ B
Rationale: De Morgan's Law: (A ∪ B)ᶜ = Aᶜ ∩ Bᶜ and (A ∩ B)ᶜ = Aᶜ ∪ Bᶜ.
Part 2: Probability
11. A single six-sided die is rolled. What is the probability of rolling an even
number?
A) 1/6
B) 1/3
C) 1/2
D) 2/3
Rationale: The even numbers are {2, 4, 6}. That's 3 favorable outcomes out of 6
total. P(Even) = 3/6 = 1/2.
2025/2026 – VERIFIED EXAM QUESTIONS
AND CORRECT SOLUTIONS WITH
RATIONALES
|| 100% GUARANTEED PASS
<LATEST VERSION>
Part 1: Set Theory & Logic
1. What is the set of all elements that are in set A or in set B or in both?
A) Intersection
B) Union
C) Complement
D) Subset
Rationale: The union of two sets, denoted A ∪ B, is defined as the set containing
all elements that are in A, or in B, or in both.
2. In a group of 50 people, 30 like coffee, and 20 like tea. If 10 like both, how
many like neither?
A) 0
B) 10
C) 20
D) 40
Rationale: Using the principle of inclusion-exclusion: |C ∪ T| = |C| + |T| - |C ∩ T|
= 30 + 20 - 10 = 40. So, 40 people like at least one drink. Therefore, 50 - 40 = 10
like neither.
3. The statement "If it is raining, then the ground is wet" is given. What is its
contrapositive?
A) If the ground is not wet, then it is not raining.
,B) If the ground is wet, then it is raining.
C) If it is not raining, then the ground is not wet.
D) It is raining and the ground is wet.
Rationale: The contrapositive of "If P, then Q" is "If not Q, then not P." It is
logically equivalent to the original statement.
4. What is the truth value of the statement: "5 > 3 AND 2 + 2 = 5"?
A) True
B) False
C) Cannot be determined
Rationale: A logical "AND" is true only if both parts are true. Since 2 + 2 = 5 is
false, the entire compound statement is false.
5. If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∩ B?
A) {1, 2, 3, 4, 5}
B) {3}
C) {1, 2}
D) { }
Rationale: The intersection (∩) is the set of elements common to both A and B.
The only common element is 3.
6. The set of all possible outcomes of an experiment is called the:
A) Event
B) Sample Space
C) Union
D) Probability Set
Rationale: By definition, the sample space is the set of all possible outcomes.
7. Which logical operator is represented by the symbol "∨"?
A) And
B) Or
C) Not
D) Implies
Rationale: In logic, "∨" is the symbol for disjunction, meaning "or".
, 8. What is the complement of set A?
A) All elements not in A, within a given universal set.
B) All elements in A.
C) The union of A with itself.
D) The intersection of A with another set.
Rationale: The complement of A, often denoted Aᶜ or A', consists of all elements
in the universal set that are not in A.
9. A truth table for a compound statement with 2 simple statements (P, Q) has
how many rows?
A) 2
B) 3
C) 4
D) 8
Rationale: The number of rows in a truth table is 2ⁿ, where n is the number of
simple statements. 2² = 4.
10. De Morgan's Law states that the complement of (A ∪ B) is equivalent to:
A) Aᶜ ∪ Bᶜ
B) A ∩ B
C) Aᶜ ∩ Bᶜ
D) A ∪ B
Rationale: De Morgan's Law: (A ∪ B)ᶜ = Aᶜ ∩ Bᶜ and (A ∩ B)ᶜ = Aᶜ ∪ Bᶜ.
Part 2: Probability
11. A single six-sided die is rolled. What is the probability of rolling an even
number?
A) 1/6
B) 1/3
C) 1/2
D) 2/3
Rationale: The even numbers are {2, 4, 6}. That's 3 favorable outcomes out of 6
total. P(Even) = 3/6 = 1/2.
