CLEP COLLEGE
MATHEMATICS PRACTICE
EXAM 2026/2027 | SCIENCE
& MATHEMATICS | 80
VERIFIED Q&A | DETAILED
RATIONALES | PASS
GUARANTEED – A+ GRADED
STUDYGUIDESOLUTIONS
,1
CLEP COLLEGE MATHEMATICS PRACTICE EXAM 2026/2027 | SCIENCE & MATHEMATICS |
80 VERIFIED Q&A | DETAILED RATIONALES | PASS GUARANTEED – A+ GRADED
SECTION A: SETS & LOGIC - Questions 1-10
Q1: Sets - Set Difference
The student is reviewing set operations. If 𝐴 = {1, 2, 3, 4, 5}and 𝐵 = {4, 5, 6, 7}, what is 𝐴 − 𝐵?
A. {1, 2, 3}
B. {4, 5}
C. {6, 7}
D. {1, 2, 3, 6, 7}
Correct Answer: A
Rationale: The set difference 𝐴 − 𝐵contains elements that are in A but not in B. So 𝐴 − 𝐵 =
{1, 2, 3}. [100% CORRECT]
Q2: Sets - Power Set
The student is reviewing power sets. If 𝐴 = {𝑥, 𝑦}, how many subsets does A have?
A. 2
B. 3
C. 4
D. 8
Correct Answer: C
Rationale: A set with 𝑛elements has 2𝑛 subsets. For 𝑛 = 2, 22 = 4: ∅, {𝑥}, {𝑦}, {𝑥, 𝑦}. [100%
CORRECT]
Q3: Sets - Cartesian Product
The student is reviewing Cartesian products. If 𝐴 = {1, 2}and 𝐵 = {𝑎, 𝑏}, what is 𝐴 × 𝐵?
A. {(1, 𝑎), (1, 𝑏), (2, 𝑎), (2, 𝑏)}
B. {(𝑎, 1), (𝑏, 1), (𝑎, 2), (𝑏, 2)}
C. {(1, 𝑎), (2, 𝑏)}
D. {(1, 2), (𝑎, 𝑏)}
Correct Answer: A
Rationale: 𝐴 × 𝐵is the set of all ordered pairs (𝑎, 𝑏)where 𝑎 ∈ 𝐴and 𝑏 ∈ 𝐵. So 𝐴 × 𝐵 =
{(1, 𝑎), (1, 𝑏), (2, 𝑎), (2, 𝑏)}. [100% CORRECT]
Q4: Logic - Tautology
, 2
The student is reviewing logic. Which statement is a tautology?
A. 𝑝 ∨ ¬𝑝
B. 𝑝 ∧ ¬𝑝
C. 𝑝 → ¬𝑝
D. 𝑝 ↔ ¬𝑝
Correct Answer: A
Rationale: A tautology is always true. 𝑝 ∨ ¬𝑝is always true (law of excluded middle). 𝑝 ∧ ¬𝑝is
always false (contradiction). [100% CORRECT]
Q5: Logic - Contradiction
The student is reviewing logic. Which statement is a contradiction?
A. 𝑝 ∨ ¬𝑝
B. 𝑝 ∧ ¬𝑝
C. 𝑝 → 𝑝
D. 𝑝 ↔ 𝑝
Correct Answer: B
Rationale: A contradiction is always false. 𝑝 ∧ ¬𝑝is always false. [100% CORRECT]
Q6: Logic - Inverse
The student is reviewing logic. What is the inverse of "If it rains, then the ground is wet"?
A. If it does not rain, then the ground is not wet.
B. If the ground is wet, then it rains.
C. If the ground is not wet, then it does not rain.
D. If it rains, then the ground is not wet.
Correct Answer: A
Rationale: The inverse of 𝑝 → 𝑞is ¬𝑝 → ¬𝑞. So "If it does not rain, then the ground is not wet."
[100% CORRECT]
Q7: Sets - Equal Sets
The student is reviewing sets. If 𝐴 = {1, 2, 3}and 𝐵 = {3, 2, 1}, which statement is true?
A. 𝐴 = 𝐵
B. 𝐴 ⊂ 𝐵
C. 𝐴 ∩ 𝐵 = ∅
D. 𝐴 ∪ 𝐵 = ∅
Correct Answer: A
Rationale: Sets are equal if they contain the same elements, regardless of order. So 𝐴 = 𝐵. [100%
CORRECT]
MATHEMATICS PRACTICE
EXAM 2026/2027 | SCIENCE
& MATHEMATICS | 80
VERIFIED Q&A | DETAILED
RATIONALES | PASS
GUARANTEED – A+ GRADED
STUDYGUIDESOLUTIONS
,1
CLEP COLLEGE MATHEMATICS PRACTICE EXAM 2026/2027 | SCIENCE & MATHEMATICS |
80 VERIFIED Q&A | DETAILED RATIONALES | PASS GUARANTEED – A+ GRADED
SECTION A: SETS & LOGIC - Questions 1-10
Q1: Sets - Set Difference
The student is reviewing set operations. If 𝐴 = {1, 2, 3, 4, 5}and 𝐵 = {4, 5, 6, 7}, what is 𝐴 − 𝐵?
A. {1, 2, 3}
B. {4, 5}
C. {6, 7}
D. {1, 2, 3, 6, 7}
Correct Answer: A
Rationale: The set difference 𝐴 − 𝐵contains elements that are in A but not in B. So 𝐴 − 𝐵 =
{1, 2, 3}. [100% CORRECT]
Q2: Sets - Power Set
The student is reviewing power sets. If 𝐴 = {𝑥, 𝑦}, how many subsets does A have?
A. 2
B. 3
C. 4
D. 8
Correct Answer: C
Rationale: A set with 𝑛elements has 2𝑛 subsets. For 𝑛 = 2, 22 = 4: ∅, {𝑥}, {𝑦}, {𝑥, 𝑦}. [100%
CORRECT]
Q3: Sets - Cartesian Product
The student is reviewing Cartesian products. If 𝐴 = {1, 2}and 𝐵 = {𝑎, 𝑏}, what is 𝐴 × 𝐵?
A. {(1, 𝑎), (1, 𝑏), (2, 𝑎), (2, 𝑏)}
B. {(𝑎, 1), (𝑏, 1), (𝑎, 2), (𝑏, 2)}
C. {(1, 𝑎), (2, 𝑏)}
D. {(1, 2), (𝑎, 𝑏)}
Correct Answer: A
Rationale: 𝐴 × 𝐵is the set of all ordered pairs (𝑎, 𝑏)where 𝑎 ∈ 𝐴and 𝑏 ∈ 𝐵. So 𝐴 × 𝐵 =
{(1, 𝑎), (1, 𝑏), (2, 𝑎), (2, 𝑏)}. [100% CORRECT]
Q4: Logic - Tautology
, 2
The student is reviewing logic. Which statement is a tautology?
A. 𝑝 ∨ ¬𝑝
B. 𝑝 ∧ ¬𝑝
C. 𝑝 → ¬𝑝
D. 𝑝 ↔ ¬𝑝
Correct Answer: A
Rationale: A tautology is always true. 𝑝 ∨ ¬𝑝is always true (law of excluded middle). 𝑝 ∧ ¬𝑝is
always false (contradiction). [100% CORRECT]
Q5: Logic - Contradiction
The student is reviewing logic. Which statement is a contradiction?
A. 𝑝 ∨ ¬𝑝
B. 𝑝 ∧ ¬𝑝
C. 𝑝 → 𝑝
D. 𝑝 ↔ 𝑝
Correct Answer: B
Rationale: A contradiction is always false. 𝑝 ∧ ¬𝑝is always false. [100% CORRECT]
Q6: Logic - Inverse
The student is reviewing logic. What is the inverse of "If it rains, then the ground is wet"?
A. If it does not rain, then the ground is not wet.
B. If the ground is wet, then it rains.
C. If the ground is not wet, then it does not rain.
D. If it rains, then the ground is not wet.
Correct Answer: A
Rationale: The inverse of 𝑝 → 𝑞is ¬𝑝 → ¬𝑞. So "If it does not rain, then the ground is not wet."
[100% CORRECT]
Q7: Sets - Equal Sets
The student is reviewing sets. If 𝐴 = {1, 2, 3}and 𝐵 = {3, 2, 1}, which statement is true?
A. 𝐴 = 𝐵
B. 𝐴 ⊂ 𝐵
C. 𝐴 ∩ 𝐵 = ∅
D. 𝐴 ∪ 𝐵 = ∅
Correct Answer: A
Rationale: Sets are equal if they contain the same elements, regardless of order. So 𝐴 = 𝐵. [100%
CORRECT]
