Which amount of postage stamp can not be formed by using 4 cent and 11 cent stamps?

5. Which amount of postage can be formed using just 4-cent and 11-cent stamps? Explanation: We can form 30 cent of postage with two 4-cent stamp and two 11-cent stamp.

What amounts of postage can be paid using only 3 and 5 stamps?

k −2 cents can be paid by using 3-cent and 5-cent stamps. Adding one 3-cent stamp, we can pay a postage of k+1 cents, i.e., P(k+1) is true. (e) Of course, in this question, it is assumed that 3-cent stamps are also available, because otherwise only postage of 5 or 10 cents can be paid.

Which amounts of postage can be made exactly using just 5-cent and 8 cent stamps?

27 cents
Putting this all together we arrive at the following fact: it is possible to (exactly) make any amount of postage greater than 27 cents using just 5-cent and 8-cent stamps.

Which amount of postage can be formed using just 4 cm and 11cm stamps?

And my conclusion is that postage of 12 + multiples of 7 can be formed with just using 4 cent stamps and 11 cent stamps.

Which of the following can only be used in disproving the statements?

Discussion Forum

Que.	Which of the following can only be used in disproving the statements?
b.	Contrapositive proofs
c.	Counter Example
d.	Mathematical Induction
	Answer:Counter Example

What is the base case for the inequality?

What is the base case for the inequality 7n > n3, where n = 3? Explanation: By the principle of mathematical induction, we have 73 > 33 ⇒ 343 > 27 as a base case and it is true for n = 3.

Which amounts of money can be formed using just 2 rupee bills and 5 rupee bills prove your answer using strong induction?

We have completed both the basis step and the inductive step, so by the principle of strong induction, the statement is true for every integer n greater than or equal to 8. What amounts of money can be formed using just two-dollar bills and five-dollar bills? Prove your answer using strong induction.

How many base cases does a proof by the weak form of the principle of mathematical induction require?

two cases
A proof by induction consists of two cases. The first, the base case (or basis), proves the statement for n = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that if the statement holds for any given case n = k, then it must also hold for the next case n = k + 1.

What is the inductive hypothesis of the proof?

The role of the induction hypothesis: The induction hypothesis is the case n = k of the statement we seek to prove (“P(k)”), and it is what you assume at the start of the induction step. You must get this hypothesis into play at some point during the proof of the induction step—if not, you are doing something wrong.

When to prove PQ true we proof P false that type of proof is known as?

Related questions 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.

Which of the following methods can be used to solve n queens problem?

6. Which of the following methods can be used to solve n-queen’s problem? Explanation: Of the following given approaches, n-queens problem can be solved using backtracking. It can also be solved using branch and bound.

How much postage can be obtained using 3 cent and 7 cent?

Use mathematical induction (and proof by division into cases) to show that any postage of at least 12 cents can be obtained using 3 cent and 7 cent stamps. I thought this was the simple kind of induction but came to realize it wasn’t. I think the term I found on the internet was strong induction.

How many 5 cent stamps are needed to make K cents?

Moreover, because k>= 12, we needed at least three 5 cent stamps to form postage of k cents. So we can replace three 5 cent stamps with four 4 cent stamps to form postage of k+1 cents. This completes the inductive step

How do you replace a 4-cent stamp with a 5-cent stamp?

*We consider two cases, when at least one 4-cent stamp has been used and where no 4-cent stamps have been used. First, suppose that at least one 4-cent stamp was used to form postage of k cents. Then we can replace this stamp with a 5-cent stamp to form postage of k+1 cents.

How to form postage of k – 3 cents using inductive hypothesis?

Using the inductive hypothesis, we can assume that P (k − 3) is true because k − 3 ≥ 12, that is, we can form postage of k − 3 cents using just 4-cent and 5-cent stamps. To form postage of k + 1 cents, we need only add another 4-cent stamp to the stamps we used to form postage of k − 3 cents.