Question

There are 1500 students in a college. Each student can be a member of three student communities namely P, Q, and R. Now using the data mentioned and the diagram given below answer the questions that follow. - Total members in community $\mathrm{P}$ is 300 . - Total members in community $\mathrm{Q}$ is 420 . - Total members in community $\mathrm{R}$ is 490 . How many students are part of at least one community? (A) 1000 (B) 1090 (C) 1110 (D) 1100

Name: Problem 4, Chapter 3: Computer Science and Information Technology
Uploaded: 2022-01-30T10:45:51-08:00
Duration: 1 min 54 s
Channel: Manik Pulyani

   There are 1500 students in a college. Each student can be a member of three student communities namely P, Q, and R. Now using the data mentioned and the diagram given below answer the questions that follow.
- Total members in community $\mathrm{P}$ is 300 .
- Total members in community $\mathrm{Q}$ is 420 .
- Total members in community $\mathrm{R}$ is 490 .
How many students are part of at least one community?
(A) 1000
(B) 1090
(C) 1110
(D) 1100

Computer Science and Information Technology

Trishna Knowledge… 2018 Edition

Chapter 3, Problem 4

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Solved by Expert Manik Pulyani

01/30/2022

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There are 1500 students in a college. Each student can be a member of three student communities namely P, Q, and R. Now using the data mentioned and the diagram given below answer the questions that follow. - Total members in community $\mathrm{P}$ is 300 . - Total members in community $\mathrm{Q}$ is 420 . - Total members in community $\mathrm{R}$ is 490 . How many students are part of at least one community? (A) 1000 (B) 1090 (C) 1110 (D) 1100

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Key Concepts

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a fundamental counting technique used to determine the size of the union of multiple sets by systematically adding and subtracting the sizes of individual sets and their intersections. This principle is crucial for avoiding overcounting when members can belong to more than one group.

Venn Diagrams

Venn diagrams are visual tools that represent the relationships between different sets using overlapping circles. They help illustrate the union, intersections, and disjoint parts of groups, making it easier to understand how different groups overlap and contribute to the total count.

Set Theory

Set theory is the study of collections of objects, often referred to as sets, and involves operations such as union and intersection. In problems involving groups like communities or clubs, set theory provides a way to organize and analyze the grouping, especially when there are overlaps between distinct groups.

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