Sets, Relations and FunctionsMCQPYQ Sep 24Question 1910 of 222
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A team has a total population of $50,000$. Out of it $28,000$ read the newspaper 'X' and $23,000$ read newspaper 'Y', while $4,000$ read both the newspaper. The number of persons not reading any of the two newspapers are:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 3,000

All Options:

  • A3,000
  • B2,000
  • C2,500
  • D5,000

Detailed Solution & Explanation

Let U\displaystyle U be the universal set representing the total population, so n(U)=50,000\displaystyle n(U) = 50,000.
Let X\displaystyle X be the set of people who read newspaper 'X', and Y\displaystyle Y be the set of people who read newspaper 'Y'. We are given:
- n(X)=28,000\displaystyle n(X) = 28,000
- n(Y)=23,000\displaystyle n(Y) = 23,000
- n(X∩Y)=4,000\displaystyle n(X \cap Y) = 4,000
The number of people who read at least one of the two newspapers is given by the union n(X∪Y)\displaystyle n(X \cup Y):
n(X∪Y)=n(X)+n(Y)−n(X∩Y)n(X \cup Y) = n(X) + n(Y) - n(X \cap Y)n(X∪Y)=28,000+23,000−4,000=47,000n(X \cup Y) = 28,000 + 23,000 - 4,000 = 47,000
The number of people who do not read either newspaper is the complement of the union, which is:
n((X∪Y)c)=n(U)−n(X∪Y)n((X \cup Y)^c) = n(U) - n(X \cup Y)n((X∪Y)c)=50,000−47,000=3,000n((X \cup Y)^c) = 50,000 - 47,000 = 3,000
Hence, **Option A** is the correct answer.

About This Chapter: Sets, Relations and Functions

Paper

Paper 3: Quantitative Aptitude

Weightage

3-5 Marks

Key Topics

Sets, Relations, Functions

This chapter covers Sets, Relations, Functions and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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