MATHEMATICAL PROOF EXAMINATION QUESTIONS AND
CORRECT ANSWER WITH EXPLANATION GRADED A+
STUDY GUIDE SOUTHERN NEW HAMPSHIRE UNIVERSITY
1. A mathematical proof is:
A. A logical argument showing truth of a statement
B. A guess
C. A diagram only
D. A calculation only
Answer: A
Rationale: Proof uses logical reasoning.
2. A theorem is:
A. A proven statement
B. A guess
C. An assumption
D. A random idea
Answer: A
Rationale: Theorems are proved true.
3. An axiom is:
A. A statement accepted without proof
B. A proven theorem
C. A contradiction
D. A calculation
Answer: A
Rationale: Basic assumptions.
4. A lemma is:
A. A helper theorem
B. A final answer
C. A guess
D. A definition
Answer: A
Rationale: Used to prove larger results.
5. A corollary is:
A. A result derived from a theorem
, B. A guess
C. A definition
D. A contradiction
Answer: A
Rationale: Follows directly.
6. Inductive reasoning moves from:
A. Specific to general
B. General to specific
C. Random to structured
D. False to true
Answer: A
Rationale: Pattern generalization.
7. Deductive reasoning moves from:
A. General to specific
B. Specific to general
C. Random to general
D. False to false
Answer: A
Rationale: Logic-based deduction.
8. A direct proof:
A. Starts from assumptions and derives result
B. Uses contradiction only
C. Uses guessing
D. Uses graphs only
Answer: A
Rationale: Straight logical steps.
9. Proof by contradiction assumes:
A. Statement is false
B. Statement is true
C. Nothing
D. Random value
Answer: A
Rationale: Leads to contradiction.
10. Proof by contrapositive proves:
A. If not Q then not P
, B. If P then Q directly
C. Random statement
D. Graph only
Answer: A
Rationale: Equivalent logic.
11. A contradiction is:
A. Logical inconsistency
B. True statement
C. Definition
D. Equation
Answer: A
Rationale: Impossible situation.
12. A proposition is:
A. Statement that can be true or false
B. Always true
C. Always false
D. Diagram
Answer: A
Rationale: Logical claim.
13. A statement is valid if:
A. It is logically proven
B. It is guessed
C. It is assumed
D. It is random
Answer: A
Rationale: Proof-based truth.
14. Logical implication is:
A. If P then Q
B. Q then P always
C. Random relation
D. Equality
Answer: A
Rationale: Conditional statement.
15. Converse of P→Q is:
A. Q→P
CORRECT ANSWER WITH EXPLANATION GRADED A+
STUDY GUIDE SOUTHERN NEW HAMPSHIRE UNIVERSITY
1. A mathematical proof is:
A. A logical argument showing truth of a statement
B. A guess
C. A diagram only
D. A calculation only
Answer: A
Rationale: Proof uses logical reasoning.
2. A theorem is:
A. A proven statement
B. A guess
C. An assumption
D. A random idea
Answer: A
Rationale: Theorems are proved true.
3. An axiom is:
A. A statement accepted without proof
B. A proven theorem
C. A contradiction
D. A calculation
Answer: A
Rationale: Basic assumptions.
4. A lemma is:
A. A helper theorem
B. A final answer
C. A guess
D. A definition
Answer: A
Rationale: Used to prove larger results.
5. A corollary is:
A. A result derived from a theorem
, B. A guess
C. A definition
D. A contradiction
Answer: A
Rationale: Follows directly.
6. Inductive reasoning moves from:
A. Specific to general
B. General to specific
C. Random to structured
D. False to true
Answer: A
Rationale: Pattern generalization.
7. Deductive reasoning moves from:
A. General to specific
B. Specific to general
C. Random to general
D. False to false
Answer: A
Rationale: Logic-based deduction.
8. A direct proof:
A. Starts from assumptions and derives result
B. Uses contradiction only
C. Uses guessing
D. Uses graphs only
Answer: A
Rationale: Straight logical steps.
9. Proof by contradiction assumes:
A. Statement is false
B. Statement is true
C. Nothing
D. Random value
Answer: A
Rationale: Leads to contradiction.
10. Proof by contrapositive proves:
A. If not Q then not P
, B. If P then Q directly
C. Random statement
D. Graph only
Answer: A
Rationale: Equivalent logic.
11. A contradiction is:
A. Logical inconsistency
B. True statement
C. Definition
D. Equation
Answer: A
Rationale: Impossible situation.
12. A proposition is:
A. Statement that can be true or false
B. Always true
C. Always false
D. Diagram
Answer: A
Rationale: Logical claim.
13. A statement is valid if:
A. It is logically proven
B. It is guessed
C. It is assumed
D. It is random
Answer: A
Rationale: Proof-based truth.
14. Logical implication is:
A. If P then Q
B. Q then P always
C. Random relation
D. Equality
Answer: A
Rationale: Conditional statement.
15. Converse of P→Q is:
A. Q→P
