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 a 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(5)

View Answer

Explanation: By induction we can prove that P(3) and P(5) is true but we can’t conclude about P(2) 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.

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