Sets, Relations and FunctionsPYQ Sept 25Question 4133 of 145
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Let S={a,b,c,d,e}\displaystyle S = \{a, b, c, d, e\}. The number of non-empty proper subsets of S is

Options

A30
B31
C32
D28
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Correct Answer

✅ Option a — 30

All Options:

  • A30
  • B31
  • C32
  • D28

Detailed Solution & Explanation

Let the set be S={a,b,c,d,e}\displaystyle S = \{a, b, c, d, e\}. The number of elements in S\displaystyle S is n=5\displaystyle n = 5.
- The total number of subsets of a set with n\displaystyle n elements is 2n\displaystyle 2^n. Here: Total subsets=25=32\text{Total subsets} = 2^5 = 32
- A **proper subset** of S\displaystyle S is any subset except the set S\displaystyle S itself. Thus: Proper subsets=2n−1=32−1=31\text{Proper subsets} = 2^n - 1 = 32 - 1 = 31
- A **non-empty proper subset** of S\displaystyle S is any proper subset except the empty set ∅\displaystyle \emptyset. Thus: Non-empty proper subsets=2n−2=32−2=30\text{Non-empty proper subsets} = 2^n - 2 = 32 - 2 = 30
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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