jjstin
Answered

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A group of 500 students were surveyed. 320 said they use Facebook, 280 said they use Instagram, and 175 said they use both. How many do not use either?

Sagot :

kenjinx

[tex]\sf{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]

[tex]\rm{\huge{ANSWER:}}[/tex]

❏ Total students: 500

❏ Use Facebook: 320

❏ Use Instagram: 280

❏ Use both: 175

❏ Total using either: 320 + 280 - 175 = 405

ׂ❏ Do not use either: 500 - 405 = [tex]\underline{\large\sf\red{95}}[/tex]

[tex]\sf\small{╰─▸ ❝ @[kenjinx]}[/tex]

[tex]\sf{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]

Zenziee

SET THEORY & PRINCIPLE OF INCLUSION-EXCLUSION

Answer:

  • 75 students

Step-by-step explanation:

In order to find the total number of students who do not use both of the social media platforms, we can apply the set of theory and the principle of inclusion-exclusion.

Let's start! First thing to do is to collect all the givens in the problem statement:

  • Total no. of students surveyed: 500
  • No. of students who use Facebook: 320
  • No. of students who use Instagram: 280
  • No. of students who use both: 175

Now that we've gathered all the necessary information, let us now proceed for the clarification of these givens by presenting them through symbols.

  • Let (|∪| = 500) - represents the total number of students surveyed.
  • Let (|A| = 320) - represents the set of students who use Facebook.
  • Let (|B| = 280) - represents the set of students who use Instagram.
  • Let (A∩B = 175) - represents the set of students who use both of these social media platforms.

Our task is to find how many students who do not use either Facebook or Instagram. But firstly, we just need to find the number of students who use Facebook or Instagram, or both before proceeding to the next step.

  • |A∪B| = |A| + |B| - |A∩B|
  • |A∪B| = 320 + 250 -175
  • |A∪B| = 600 - 175
  • |A∪B| = 425

Next and the last step, we need to calculate what the given problem wants.

  • |∪ - (A∪B)| = |∪| - |A∪B|
  • |∪ - (A∪B)| = 500 - 425
  • |∪ - (A∪B)| = 75

Therefore, there are 75 students who do not use either Facebook or Instagram.

View image Zenziee
Zenziee

SET THEORY & PRINCIPLE OF INCLUSION-EXCLUSION

Answer:

  • 75 students

Step-by-step explanation:

In order to find the total number of students who do not use both of the social media platforms, we can apply the set of theory and the principle of inclusion-exclusion.

Let's start! First thing to do is to collect all the givens in the problem statement:

  • Total no. of students surveyed: 500
  • No. of students who use Facebook: 320
  • No. of students who use Instagram: 280
  • No. of students who use both: 175

Now that we've gathered all the necessary information, let us now proceed for the clarification of these givens by presenting them through symbols.

  • Let (|∪| = 500) - represents the total number of students surveyed.
  • Let (|A| = 320) - represents the set of students who use Facebook.
  • Let (|B| = 280) - represents the set of students who use Instagram.
  • Let (A∩B = 175) - represents the set of students who use both of these social media platforms.

Our task is to find how many students who do not use either Facebook or Instagram. But firstly, we just need to find the number of students who use Facebook or Instagram, or both before proceeding to the next step.

  • |A∪B| = |A| + |B| - |A∩B|
  • |A∪B| = 320 + 250 -175
  • |A∪B| = 600 - 175
  • |A∪B| = 425

Next and the last step, we need to calculate what the given problem wants.

  • |∪ - (A∪B)| = |∪| - |A∪B|
  • |∪ - (A∪B)| = 500 - 425
  • |∪ - (A∪B)| = 75

Therefore, there are 75 students who do not use either Facebook or Instagram.

View image Zenziee
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