Discrete Mathematics Questions and Answers – Strong Induction and Well-Ordering

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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Strong Induction and Well-Ordering”.

1. A polygon with 7 sides can be triangulated into ________
a) 7
b) 14
c) 5
d) 10
View Answer

Answer: c
Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.
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2. Every simple polynomial has an interior diagonal.
a) True
b) False
View Answer

Answer: a
Explanation: By using Strong Induction.

3. A polygon with 12 sides can be triangulated into _______
a) 7
b) 10
c) 5
d) 12
View Answer

Answer: b
Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.

4. Let P(n) be the statement that postage of n cents can be formed using just 3-cents stamps and 5-cents stamps. Is the statements P(8) and P(10) are Correct?
a) True
b) False
View Answer

Answer: a
Explanation: We can form 8 cent of postage with one 3-cent stamp and one 5-cent stamp. P(10) is true because we can form it using two 5-cent stamps.

5. Which amount of postage can be formed using just 4-cent and 11-cent stamps?
a) 2
b) 5
c) 30
d) 10
View Answer

Answer: d
Explanation: We can form 30 cent of postage with two 4-cent stamp and two 11-cent stamp.
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6. 22-cent of postage can be produced with two 4-cent stamp and one 11-cent stamp.
a) True
b) False
View Answer

Answer: b
Explanation: By using two 4-cent stamp and one 11-cent stamp, 27-cent postage is produced.

7. Which amount of postage can be formed using just 3-cent stamp and 10-cent stamps?
a) 27
b) 20
c) 11
d) 5
View Answer

Answer:a
Explanation: We can form 27 cent of postage with nine 3-cent stamp and 20-cent postage can be formed by using two 10-cent stamps.

8. Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n+2) is true.
a) P(3)
b) P(2)
c) P(4)
d) P(6)
View Answer

Answer: a
Explanation: By induction we can prove that P(3) is true but we can’t conclude about P(2), p(6) and P(4).

9. Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true.
a) P(1)
b) P(2)
c) P(4)
d) P(n)
View Answer

Answer: d
Explanation: By induction, we can prove that P(n) is true.
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10. A polygon with 25 sides can be triangulated into _______
a) 23
b) 20
c) 22
d) 21
View Answer

Answer: a
Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn