Sets, Relations and FunctionsMCQPYQ Nov. 19Question 1961 of 217
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If A={a,b,c,d}\displaystyle A = \{a, b, c, d\}, B={p,q,r,s}\displaystyle B = \{p, q, r, s\} which of the following relation is a function from A\displaystyle A to B\displaystyle B

Options

AR1={(p,a),(b,q),(c,s)}\displaystyle R_1 = \{(p,a), (b,q), (c,s)\}
BR2={(p,a),(b,r),(d,s)}\displaystyle R_2 = \{(p,a), (b,r), (d,s)\}
CR3={(b,p),(c,s),(b,r)}\displaystyle R_3 = \{(b,p), (c,s), (b,r)\}
DR4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}
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Correct Answer

✅ Option d — R4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}

All Options:

  • AR1={(p,a),(b,q),(c,s)}\displaystyle R_1 = \{(p,a), (b,q), (c,s)\}
  • BR2={(p,a),(b,r),(d,s)}\displaystyle R_2 = \{(p,a), (b,r), (d,s)\}
  • CR3={(b,p),(c,s),(b,r)}\displaystyle R_3 = \{(b,p), (c,s), (b,r)\}
  • DR4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}

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Detailed Solution & Explanation

We are given sets A={a,b,c,d}\displaystyle A = \{a, b, c, d\} and B={p,q,r,s}\displaystyle B = \{p, q, r, s\}.
A relation from A\displaystyle A to B\displaystyle B is a function if every element of the domain A\displaystyle A appears exactly once as the first component in the ordered pairs of the relation.
Let's test each option:
- **Option A**: R1={(p,a),(b,q),(c,s)}\displaystyle R_1 = \{(p,a), (b,q), (c,s)\}. The first component p\displaystyle p does not belong to the domain A\displaystyle A. So R1\displaystyle R_1 is not a relation from A\displaystyle A to B\displaystyle B.
- **Option B**: R2={(p,a),(b,r),(d,s)}\displaystyle R_2 = \{(p,a), (b,r), (d,s)\}. The first component p∉A\displaystyle p \notin A. So R2\displaystyle R_2 is not a relation from A\displaystyle A to B\displaystyle B.
- **Option C**: R3={(b,p),(c,s),(b,r)}\displaystyle R_3 = \{(b,p), (c,s), (b,r)\}. The element b\displaystyle b is mapped to two different values p\displaystyle p and r\displaystyle r. Also, elements a\displaystyle a and d\displaystyle d have no images. So R3\displaystyle R_3 is not a function.
- **Option D**: R4={(a,p),(b,r),(c,q),(d,s)}\displaystyle R_4 = \{(a,p), (b,r), (c,q), (d,s)\}. Every element of A={a,b,c,d}\displaystyle A = \{a, b, c, d\} appears exactly once as the first component, and all second components belong to B\displaystyle B. Therefore, R4\displaystyle R_4 is a function.
Hence, **Option D** 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.

Key Concepts to Understand

Function

A relation from a set A (Domain) to a set B (Codomain) such that every element in A is associated with exactly one element in B. Written as f: A→B. Types include Linear, Quadratic, Polynomial, and Exponential functions.

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