Question

nt or the data of the variable, if the value of the original variable is the method there, I 24 January 1980 and 20 dst Student ID: Name: M. De Vna 1.

1.60 people use SNS which 25 people using Facebook, 26 people using LINE, 26 people using Instagram, there are people using Facebook and LINE 9 people, 11 people using LINE and Instagram, 8 people using Facebook and Instagram,

There are 8 people who do not use SNS,

a.)Calculate the number of people using three SNS

b.)find the number of people using just one SNS)

  2. From the set X = {1,2, 101} find out how many ways to select a two number whose sum is an even number, and how many ways to select two number that will have sum odd number?

please explan thanks

  

Answer 1

1. Let the set of people:

• Using social networking sites be S. Then the people not using them make the set .
• Using Facebook be F.
• Using LINE be L.
• Using Instagram be I.

Now, we know that the number of people using social networking sites is 60. Then, n(S)=60. The number of people not using social networking sites is 8. So, n()=8. Similarly, from the given data, n(F)=25, n(L)=26, n(I)=26.

The number of people using Facebook and LINE are 9. Therefore, n()=9. Similarly, n()=11, n()=8.

The diagram below shows the

• Blue circle as the area of people using Facebook
• Brown circle as the area of people using LINE
• Red circle as the area of people using Instagram.

All the isolated sections in the diagram have been named using numbers. Since Facebook, Instagram and LINE are the only social networking sites being used here, the area covered by all three circles is the total area of people using social networking sites. Then the numbered areas under:

• F are 1, 2, 6, 7
• I are 2, 3, 4, 7
• L are 4, 5, 6, 7
• S are 1, 2, 3, 4, 5, 6, 7, which is also the set
• is 8.
• are 6, 7
• are 4, 7
• are 2, 7
• is 7

(a) Now, the set of people using three social networking sites is the set of people using Facebook and Instagram and LINE. Then, this set is given by . Now, in terms of numbered areas,

=1+2+3+4+5+6+7

NOTE: THESE NUMBERS ARE NOT FOR CALCULATIONS,

BUT SIMPLY FOR THE PURPOSE OF LABELING.

=(1+2+6+7)+3+4+5

=F+3+4+5

=F+(2+3+4+7)+5-2-7

=F+I+5-2-7

=F+I+(4+5+6+7)-2-7-4-6-7

=F+I+L-2-7-4-6-7

=F+I+L-(2+7)-(4+7)-(6+7)+7

=F+I+L-()-()-()+7

=F+I+L-()-()-()+()

So, we have =F+I+L-()-()-()+()

Then, n()=n(F)+n(I)+n(L)-n()-n()-n()+n()

NOTE: THE FOLLOWING NUMBERS ARE

FOR CALCULATION PURPOSES.

=> 60=25+26+26-8-11-9+n()

=>n()=11.

Therefore, the number of people using all three social networking sites are 11.

(b) Now, from the diagram, we can see that the area of people using Facebook are given by the numbered areas 1,2,6,7.

Among these, 2 and 7 are people using both Facebook and Instagram, and 6 and 7 are people using both Facebook and LINE. So, the area 1 gives us the number of people using ONLY Facebook. Similarly, area 3 gives us the number of people sing ONLY Instagram, and area 5 gives us the number of people using ONLY LINE. Then, the number of people using just one social networking site,i.e., either ONLY Facebook, or ONLY Instagram, or ONLY LINE, is given by the areas 1, 3, 5.

Now, =1+2+3+4+5+6+7

NOTE: THESE NUMBERS ARE NOT FOR CALCULATIONS,

BUT SIMPLY FOR THE PURPOSE OF LABELING.

=(1+3+5)+(2+7)+(4+7)+(6+7)-7-7

=(1+3+5)+()+()+()-()-()

Then, n()=n(1+3+5)+n()+n()+n()-n()-n()

=> n(1+3+5)=n()-n()-n()-n()+n()+n()

NOTE: THE FOLLOWING NUMBERS ARE

FOR CALCULATION PURPOSES.

=60-9-11-8+11+11

=54

Therefore, 54 people use JUST ONE social networking site.

2. The set we have is X={1, 2, 101}.

NOTE: I am assuming the selection of numbers mentioned in the problem is free from ordering.

For two numbers to have their sum as an even number, the two numbers either have to be both odd, or both even. It cannot be a set of one odd an one even number. In the set, we have two odd numbers 1 and 101, and only one even number, 2. Therefore, we cannot select two even numbers from the set. We can, however select two odd numbers 1 and 101 from the set. Also, the set has exactly two odd numbers. So, there is only one possible pair of odd numbers, and hence only one way to select them, i.e., (1,101) (not ordered) whose sum is 102, which is an even number.

Therefore, there is EXACTLY ONE way to select two numbers from the set X={1,2,101} whose sum is an even number.

Now, for two numbers to have their sum as an odd number, one of the numbers has to be odd, and the other has to be even. We cannot have a pair of both odd or both even numbers. Now, there is only one even number in the set to choose from, i.e., 2, and two odd numbers 1 and 101 to choose from. Since we must have one even number in the pair, 2 will be the even number in every possible pair. Now, we need an odd number to pair with 2, and we have two options: 1 and 101. So, the possible pairs are (2,1) and (2,101) (not ordered), with sums 3 and 103 respectively, both of which are odd numbers.

Therefore, there are TWO ways to select two numbers from the set X={1,2,101} whose sum is an odd number.