MFC-UNIT-1-2. Strong Induction and Well Ordering

Strong Induction and Well Ordering
1.        1	A polygon with 7 sides can be triangulated into ________ a) 7 b) 14 c) 5 d) 10 Answer: c Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.	C
2.        2	A polygon with 12 sides can be triangulated into _______ a) 7 b) 10 c) 5 d) 12 Answer: b Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.	B
3.        3	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) 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).	A
4.        4	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) Answer: d Explanation: By induction, we can prove that P(n) is true.	D
5.        5	10. A polygon with 25 sides can be triangulated into _______ a) 23 b) 20 c) 22 d) 21 Answer: a Explanation: A simple polygon with n sides can be triangulated into n-2 triangles, where n > 2.	A
6.        6	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) 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).	A
7.        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 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.	A
8.        8	Which amount of postage can be formed using just 4-cent and 11-cent stamps? a) 2 b) 5 c) 30 d) 10 Answer: d Explanation: We can form 30 cent of postage with two 4-cent stamp and two 11-cent stamp.	D