In class of 50 students the number of students who offer Economic 10 students offer neither of the two subject and 5 students offer both subjects

Question

1.illustrate the information on Venn diagram
2.How many students offer accounting
3, How many students offer Economic
4. How many students offer only one subjects
Find the solution of this question

Answer 1

Let's break down the information given step by step and then answer the questions.

1. Understanding the Information:

   • Total number of students = 50
   • Students who offer neither subject = 10
   • Students who offer both subjects = 5
   • Let \( A \) be the set of students who offer Accounting.
   • Let \( E \) be the set of students who offer Economics.

2. Finding Students Offering at Least One Subject: \[ \text{Students offering at least one subject} = \text{Total Students} - \text{Students offering neither} = 50 - 10 = 40 \]

3. Using the Information for a Venn Diagram: Let's assume:

• \( n(A) \) = number of students offering Accounting
• \( n(E) \) = number of students offering Economics

From the information provided, we can represent it in a Venn diagram:

• Students in both sets (intersection): 5 (students who offer both subjects)

4. Setting Up the Equation: The formula for the union of two sets is: \[ n(A \cup E) = n(A) + n(E) - n(A \cap E) \] Where:

• \( n(A \cup E) \) = students offering at least one subject = 40
• \( n(A \cap E) \) = students offering both subjects = 5

Thus, we have: \[ 40 = n(A) + n(E) - 5 \] This simplifies to: \[ n(A) + n(E) = 45 \quad \text{(1)} \]

5. Finding Students Who Offer Only One Subject: Let:

• \( n(A) \) = students who only offer Accounting
• \( n(E) \) = students who only offer Economics

From the accounting and economics students:

• Students who offer only Accounting = \( n(A) - 5 \)
• Students who offer only Economics = \( n(E) - 5 \)

So, the number of students who offer only one subject is given by: \[ \text{Only Accounting} + \text{Only Economics} = (n(A) - 5) + (n(E) - 5) \] \[ = n(A) + n(E) - 10 \]

Now substituting from equation (1): \[ = 45 - 10 = 35 \]

6. Finding the Number of Students Offering Accounting and Economics: Without additional information about the specific values of \( n(A) \) and \( n(E) \), we cannot determine the exact counts of students in each individual subject from the provided information.

To summarize, the answers to the questions are:

1. A Venn diagram would have two circles intersecting (one for Accounting, one for Economics), with "5" in the intersection, and the rest would depend on individual subject counts which are indeterminate with the given info.
2. Number of students offering Accounting: \( n(A) \)
3. Number of students offering Economics: \( n(E) \)
4. Number of students offering only one subject: 35

To find exact counts for Accounting and Economics, we would ideally need one more piece of information (e.g., the total number of students taking Accounting, or students taking Economics only).