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
Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.
2. Every simple polynomial has an interior diagonal.
a) True
b) False
View Answer
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
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
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
Explanation: We can form 30 cent of postage with two 4-cent stamp and two 11-cent stamp.
6. 22-cent of postage can be produced with two 4-cent stamp and one 11-cent stamp.
a) True
b) False
View Answer
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
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
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
Explanation: By induction, we can prove that P(n) is true.
10. A polygon with 25 sides can be triangulated into _______
a) 23
b) 20
c) 22
d) 21
View Answer
Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.
Sanfoundry Global Education & Learning Series – Discrete Mathematics
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