Sets, Relations and FunctionsMCQPYQ Jun 23Question 1904 of 222
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If A={a,b,c}\displaystyle A = \{a, b, c\}, B={b,c,d}\displaystyle B = \{b, c, d\} and C={a,d}\displaystyle C = \{a, d\} then (A−B)×(B∩C)\displaystyle (A - B) ×\displaystyle \times (B \cap C) is equal to:

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

✅ Option b — (a,c),(d,d)\displaystyle (a,c), (d,d)

All Options:

  • A(a,d),(c,d)\displaystyle (a,d), (c,d)
  • B(a,c),(d,d)\displaystyle (a,c), (d,d)
  • C(c,a),(d,a)\displaystyle (c,a), (d,a)
  • D(a,d),(b,d)\displaystyle (a,d), (b,d)

Detailed Solution & Explanation

Given sets:
A={a,b,c}\displaystyle A = \{a, b, c\}
B={b,c,d}\displaystyle B = \{b, c, d\}
C={a,d}\displaystyle C = \{a, d\}
First, let us find the difference set (A−B)\displaystyle (A - B) which contains elements in A\displaystyle A but not in B\displaystyle B:
A−B={a}A - B = \{a\}
Next, let us find the intersection (B∩C)\displaystyle (B \cap C) which contains elements common to B\displaystyle B and C\displaystyle C:
B∩C={d}B \cap C = \{d\}
Now, we compute the Cartesian product (A−B)×(B∩C)\displaystyle (A - B) ×\displaystyle \times (B \cap C):
(A−B)×(B∩C)={a}×{d}={(a,d)}(A - B) ×\displaystyle \times (B \cap C) = \{a\} ×\displaystyle \times \{d\} = \{(a, d)\}
Mathematically, the correct set is {(a,d)}\displaystyle \{(a, d)\}. However, the textbook options are:
- Option A: {(a,d),(c,d)}\displaystyle \{(a, d), (c, d)\}
- Option B: {(a,c),(d,d)}\displaystyle \{(a, c), (d, d)\}
- Option C: {(c,a),(d,a)}\displaystyle \{(c, a), (d, a)\}
- Option D: {(a,d),(b,d)}\displaystyle \{(a, d), (b, d)\}
None of the options lists the exact set {(a,d)}\displaystyle \{(a, d)\}. In the official key, the correct choice is marked as **Option B**. This represents a typographical error in the textbook.
Hence, **Option B** 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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