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Induction Proof

If n >= 1, the number of strings using the digits 0,1, and 2 with no two consecutive places holding the same digit, is 3x2^n-1. For example, there are 12 such strings of length three: 010, 012, 020, 021, 101, 102, 120, 121, 201, 202, 210, and 212. Prove this claim by induction on the length of the strings. Is the formula true for n=0?

Subject:

Math

Topic:

Discrete Structures

Posting ID:

25320

OTA ID:

101298

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Induction Problem

Attached in word document Numbers of the form tn = n (n+1) / 2 are called triangular numbers, because marbles arranged in an equilateral triangle, n on a side, will total... (see attachment)

Subject:

Math

Topic:

Discrete Structures

Posting ID:

25328

OTA ID:

104455

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Error Correcting Code

If no two strings in a code differ in fewer than three positions, the we can actually correct a single error, by finding the unique string in the code that differs from the received string in only one position. It turns out that there is a code of 7-bit strings that corrects single errors and contains 16 strings. Find such a code. Hint: Reasoning it out is probably best, but if you get stuck, write a program that searches for the string. From the example in the book - the strings would be like ASCII sequence of bits - whereby ASCII has a seven bit code and then a parity bit placed on the front for error detecting.

Subject:

Math

Topic:

Discrete Structures

Posting ID:

25365

OTA ID:

104572

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Recursive definition

We can define sorted lists of integers as follows: BASIS - A list consisting of a single integer is sorted. INDUCTION - If L is a sorted list in which the last element is a and if b >= a, then L followed by b is a sorted list. Prove that this recursive definition of "sorted list" is equivalent to our original, nonrecursive definition, which is that the list consist of integers a1 <= a2 <= .... <= an Remember, you need to prove to parts: (a) If a list is sorted by the recursive definition, then it is sorted by the nonrecursive definition (b) if a list is sorted by the nonrecursive definition, then it is sorted by the recursive definition. Part(a) can use induction on... click for more

Subject:

Math

Topic:

Discrete Structures

Posting ID:

25366

OTA ID:

104455

View Details $1.99 Download Add to Cart

Induction by recursion

Define recursively the set of even-parity strings, by induction on the length of the string. Hint: It helps to define two concepts simultaneously, both the even-parity and odd-parity strings.

Subject:

Math

Topic:

Discrete Structures

Posting ID:

25422

OTA ID:

104459

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