In a class of 25 students of Mathematics and Economics, 12...

Name: Problem 84, Chapter 4: Business Mathematics and Statistics
Uploaded: 2021-06-23T21:38:14-08:00
Duration: 1 min 36 s
Channel: Aman Gupta
Description: In a class of 25 students of Mathematics and Economics, 12 students have taken Mathematics and 8 have taken Mathematics but not Economics. Find the number of students who have both Mathematics and Economics, and the number who have taken Economics but not Mathematics.

In a class of 25 students of Mathematics and Economics, 12 students have taken Mathematics and 8 have taken Mathematics but not Economics. Find the number of students who have both Mathematics and Economics, and the number who have taken Economics but not Mathematics.

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Key Concepts

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a key counting technique in set theory and combinatorics that helps determine the total number of elements in the union of overlapping sets by subtracting the elements that have been counted more than once in the overlaps.

Set Difference

The concept of set difference refers to the elements that are present in one set but not in another. This is important when calculating the number of elements exclusive to one category when there is a known overlap with another category.

Set Theory

Set theory is a fundamental branch of mathematics that deals with the study of collections of objects, known as sets. It provides the basic language and tools for discussing groups of elements, which includes concepts like unions, intersections, complements, and differences between sets.

Venn Diagrams

Venn diagrams are visual representations used in set theory to illustrate the relationships between different sets. They show how sets overlap or are mutually exclusive by depicting intersections (overlaps), unions, and complements, making complex relationships easier to understand.

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