Math Problem Statement

In a group of students 30 read mathematics, 24 read economics, 22 read statistics, 14 read mathematics only, 8 read economics only, 6 read mathematics and statistics only, 2 read mathematics and economics only and 8 read none of these subjects? How many students are there in the group? show in venn diagram

Solution

Here is the Venn diagram representing the distribution of students in the group based on their subjects. It shows the number of students in each category: Mathematics, Economics, Statistics, and their various intersections.

Would you like to go over any further details or have additional questions about this problem?

Here are a few related questions:

  1. How can we apply this method to solve problems involving more than three sets?
  2. What happens if the numbers for each subject overlap differently?
  3. How can Venn diagrams help visualize probabilities in statistics?
  4. How do we interpret a Venn diagram with non-overlapping sets?
  5. What are some other mathematical tools used to represent set operations?

Tip: When dealing with Venn diagrams, always start by defining the unknowns for the intersections and use the given total numbers for each set to form equations. This will simplify solving for the unknowns.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Counting Principles

Formulas

Total students = Mathematics only + Economics only + Statistics only + (Mathematics and Statistics only) + (Mathematics and Economics only) + (All three subjects) + None of the subjects

Theorems

Inclusion-Exclusion Principle

Suitable Grade Level

Grades 9-11