CLEP COLLEGE
MATHEMATICS EXAM
2026/2027 | SCIENCE &
MATHEMATICS | 100
VERIFIED Q&A | DETAILED
RATIONALES | PASS
GUARANTEED – A+ GRADED
STUDYGUIDESOLUTIONS
,1
CLEP COLLEGE MATHEMATICS EXAM 2026/2027 | SCIENCE & MATHEMATICS | 100
VERIFIED Q&A | DETAILED RATIONALES | PASS GUARANTEED – A+ GRADED
SECTION A: SETS & LOGIC - Questions 1-15
Q1: Sets - Union
The student is reviewing set operations. If 𝐴 = {1, 2, 3, 4}and 𝐵 = {3, 4, 5, 6}, what is 𝐴 ∪ 𝐵?
A. {3, 4}
B. {1, 2, 3, 4, 5, 6}
C. {1, 2, 5, 6}
D. {1, 2, 3, 4}
Correct Answer: B
Rationale: The union 𝐴 ∪ 𝐵contains all elements that are in A or B (or both). So 𝐴 ∪ 𝐵 =
{1, 2, 3, 4, 5, 6}. [100% CORRECT]
Q2: Sets - Intersection
The student is reviewing set operations. If 𝐴 = {1, 2, 3, 4}and 𝐵 = {3, 4, 5, 6}, what is 𝐴 ∩ 𝐵?
A. {3, 4}
B. {1, 2, 3, 4, 5, 6}
C. {1, 2, 5, 6}
D. ∅
Correct Answer: A
Rationale: The intersection 𝐴 ∩ 𝐵contains elements that are in both A and B. So 𝐴 ∩ 𝐵 = {3, 4}.
[100% CORRECT]
Q3: Sets - Complement
The student is reviewing set operations. If universal set 𝑈 = {1, 2, 3, 4, 5, 6, 7, 8}and 𝐴 = {1, 3, 5, 7},
what is 𝐴′ (complement of A)?
A. {2, 4, 6, 8}
B. {1, 3, 5, 7}
C. {1, 2, 3, 4, 5, 6, 7, 8}
D. ∅
Correct Answer: A
Rationale: The complement of A contains all elements in U that are not in A. So 𝐴′ = {2, 4, 6, 8}.
[100% CORRECT]
Q4: Sets - Subset
, 2
The student is reviewing set relationships. If 𝐴 = {1, 2}and 𝐵 = {1, 2, 3, 4}, which statement is true?
A. 𝐴 ⊂ 𝐵
B. 𝐵 ⊂ 𝐴
C. 𝐴 = 𝐵
D. 𝐴 ∩ 𝐵 = ∅
Correct Answer: A
Rationale: Every element of A is in B, and B has elements not in A, so A is a proper subset of B: 𝐴 ⊂
𝐵. [100% CORRECT]
Q5: Sets - Cardinality
The student is reviewing cardinality. If 𝐴 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒}, what is ∣ 𝐴 ∣?
A. 4
B. 5
C. 6
D. 10
Correct Answer: B
Rationale: The cardinality ∣ 𝐴 ∣is the number of elements in set A. There are 5 elements. [100%
CORRECT]
Q6: Logic - Negation
The student is reviewing logic. What is the negation of the statement "All students study"?
A. No students study.
B. Some students do not study.
C. All students do not study.
D. Some students study.
Correct Answer: B
Rationale: The negation of "All students study" is "Some students do not study" (at least one student
does not study). [100% CORRECT]
Q7: Logic - Conjunction
The student is reviewing logic. If 𝑝is true and 𝑞is false, what is the truth value of 𝑝 ∧ 𝑞?
A. True
B. False
C. Cannot be determined
D. Both true and false
Correct Answer: B
Rationale: The conjunction 𝑝 ∧ 𝑞is true only if both p and q are true. Since q is false, 𝑝 ∧ 𝑞is false.
[100% CORRECT]
MATHEMATICS EXAM
2026/2027 | SCIENCE &
MATHEMATICS | 100
VERIFIED Q&A | DETAILED
RATIONALES | PASS
GUARANTEED – A+ GRADED
STUDYGUIDESOLUTIONS
,1
CLEP COLLEGE MATHEMATICS EXAM 2026/2027 | SCIENCE & MATHEMATICS | 100
VERIFIED Q&A | DETAILED RATIONALES | PASS GUARANTEED – A+ GRADED
SECTION A: SETS & LOGIC - Questions 1-15
Q1: Sets - Union
The student is reviewing set operations. If 𝐴 = {1, 2, 3, 4}and 𝐵 = {3, 4, 5, 6}, what is 𝐴 ∪ 𝐵?
A. {3, 4}
B. {1, 2, 3, 4, 5, 6}
C. {1, 2, 5, 6}
D. {1, 2, 3, 4}
Correct Answer: B
Rationale: The union 𝐴 ∪ 𝐵contains all elements that are in A or B (or both). So 𝐴 ∪ 𝐵 =
{1, 2, 3, 4, 5, 6}. [100% CORRECT]
Q2: Sets - Intersection
The student is reviewing set operations. If 𝐴 = {1, 2, 3, 4}and 𝐵 = {3, 4, 5, 6}, what is 𝐴 ∩ 𝐵?
A. {3, 4}
B. {1, 2, 3, 4, 5, 6}
C. {1, 2, 5, 6}
D. ∅
Correct Answer: A
Rationale: The intersection 𝐴 ∩ 𝐵contains elements that are in both A and B. So 𝐴 ∩ 𝐵 = {3, 4}.
[100% CORRECT]
Q3: Sets - Complement
The student is reviewing set operations. If universal set 𝑈 = {1, 2, 3, 4, 5, 6, 7, 8}and 𝐴 = {1, 3, 5, 7},
what is 𝐴′ (complement of A)?
A. {2, 4, 6, 8}
B. {1, 3, 5, 7}
C. {1, 2, 3, 4, 5, 6, 7, 8}
D. ∅
Correct Answer: A
Rationale: The complement of A contains all elements in U that are not in A. So 𝐴′ = {2, 4, 6, 8}.
[100% CORRECT]
Q4: Sets - Subset
, 2
The student is reviewing set relationships. If 𝐴 = {1, 2}and 𝐵 = {1, 2, 3, 4}, which statement is true?
A. 𝐴 ⊂ 𝐵
B. 𝐵 ⊂ 𝐴
C. 𝐴 = 𝐵
D. 𝐴 ∩ 𝐵 = ∅
Correct Answer: A
Rationale: Every element of A is in B, and B has elements not in A, so A is a proper subset of B: 𝐴 ⊂
𝐵. [100% CORRECT]
Q5: Sets - Cardinality
The student is reviewing cardinality. If 𝐴 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒}, what is ∣ 𝐴 ∣?
A. 4
B. 5
C. 6
D. 10
Correct Answer: B
Rationale: The cardinality ∣ 𝐴 ∣is the number of elements in set A. There are 5 elements. [100%
CORRECT]
Q6: Logic - Negation
The student is reviewing logic. What is the negation of the statement "All students study"?
A. No students study.
B. Some students do not study.
C. All students do not study.
D. Some students study.
Correct Answer: B
Rationale: The negation of "All students study" is "Some students do not study" (at least one student
does not study). [100% CORRECT]
Q7: Logic - Conjunction
The student is reviewing logic. If 𝑝is true and 𝑞is false, what is the truth value of 𝑝 ∧ 𝑞?
A. True
B. False
C. Cannot be determined
D. Both true and false
Correct Answer: B
Rationale: The conjunction 𝑝 ∧ 𝑞is true only if both p and q are true. Since q is false, 𝑝 ∧ 𝑞is false.
[100% CORRECT]
