Exercise 3.7.1: Proving statements about odd and even integers with direct proofs. info About Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k 1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer.

The question is incomplete. The complete question is :

Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd. (b) The product of two odd integers is an odd integer.

Solution :

Odd number integers = 2k + 1, where k is integer

Even number integer = 2k

a). Odd integer + even integer

  = 2k + 1 + 2k

 = 4k + 1

  = 2(2k) + 1

Let 2k = t, where t is integer

   = 2t + 1

  = Odd integer by definition

If number is 2t + 1 where t belongs to integer, then it is odd integer.

Hence proved.

b). Product of two odd integers :     where belongs to integer.

Let and

here, a and b belongs to integers since and are integers.

We get:

2a+2b+1

= 2(a+b)+1

= 2l + 1,             Let (a+b)=l and l belongs to integers.

It is odd integer by definition.

Hence proved.

A code in C++ follows:

Explanation:

#include<iostream>

using namespace std;

int calculate_area(int width, int length)

{

int area;

area=width*length;

return area;

}

int main()

{

int a,b,ar,c,d,ar1,n;

cout<<"\nEnter length of room:";

cin>>a;

cout<<"\nEnter width of room:";

cin>>b;

ar=calculate_area(a,b);

cout<<"\nArea of room:"<<ar<<" units";

cout<<"\nEnter length of mat:";

cin>>c;

cout<<"\nEnter width of mat:";

cin>>d;

ar1=calculate_area(c,d);

n=ar/ar1;

cout<<"\nNumber of mats required are:"<<n;

return 0;

}

def get_word(sentence, n):

# Only proceed if n is positive

   if n > 0:

       words = sentence.split()

# Only proceed if n is not more than the number of words

       if n <= len(words):

           return words[n-1]

   return (" ")

print(get_word("This is a lesson about lists", 4)) # Should print: lesson

print(get_word("This is a lesson about lists", -4)) # Nothing

print(get_word("Now we are cooking!", 1)) # Should print: Now

print(get_word("Now we are cooking!", 5)) # Nothing

Explanation:

Added parts are highlighted.

If n is greater than 0, split the given sentence using split method and set it to the words.

If n is not more than the number of words, return the (n-1)th index of the words. Since the index starts at 0, (n-1)th index corresponds to the nth word

The technology that could be partnered with Cloud to allow the international fast-food chain to gain insights into customer data, including location and order patterns, is called data analytics or big data analytics. It involves using software algorithms and tools to analyze large and complex datasets like customer data, and extract useful insights and patterns that can be used to make informed decisions about customer-focused experiences such as promotions and unique user experiences. Data analytics can help businesses improve customer satisfaction, increase sales and revenue, and gain a competitive advantage in the marketplace.

Question:

When multiple team members are working on a related feature, how often should they integrate their work

Select only one answer.

A) Do the integration midway through the iteration.

B) After they reach a logical end of creating the functionality.

C) In a scheduled daily (or multiple times in a day) frequency.

D) In a scheduled weekly (or multiple times in a week) frequency.

The best option is D.

Explanation:

Multiple integrations per day may become too cumbersome. Leaving the various parts of the project until a logical end for a functionality has been reached may create room for a lot of errors thus resulting in time wasted.

To ensure regular course correction (if required), twice a week would suffice.

Cheers!

Data Security

Yes, Bob is correct that only 8 months is required to pay off the amount of $200 for the ticket.

Given that,

Based on the above information, the calculation is as follows:

= $25 × 8 months

= $200

Therefore we can conclude that yes, Bob is correct that only 8 months is required to pay off the amount of $200 for the ticket.

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