Set, Relations and FunctionsPYQ Nov. 18Question 1959 of 217
All Questions

Identify the function from the following: (1,1), (1,2), (1,3)

Options

A(1,1), (2,1), (2,3)
B(1,1), (2,2), (3,2), (4,2)
CNone of these
D(1,1), (1,2), (2,3), (3,2)
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Correct Answer

✅ Option b — (1,1), (2,2), (3,2), (4,2)

All Options:

  • A(1,1), (2,1), (2,3)
  • B(1,1), (2,2), (3,2), (4,2)
  • CNone of these
  • D(1,1), (1,2), (2,3), (3,2)

Detailed Solution & Explanation

A relation f\displaystyle f from a set X\displaystyle X to Y\displaystyle Y is a function if every element x\displaystyle x in the domain has a unique image y\displaystyle y in the codomain (i.e., no two distinct ordered pairs in the relation have the same first component).
Let's analyze the options:
- **Option A**: {(1,1),(2,1),(2,3)}\displaystyle \{(1,1), (2,1), (2,3)\}. The first component `2` is mapped to two different values: `1` and `3`. So it is not a function.
- **Option B**: {(1,1),(2,2),(3,2),(4,2)}\displaystyle \{(1,1), (2,2), (3,2), (4,2)\}. The first components are {1,2,3,4}\displaystyle \{1, 2, 3, 4\}, all of which are distinct and unique. Each input maps to exactly one output. Thus, this **is a function**.
- **Option D**: {(1,1),(1,2),(2,3),(3,2)}\displaystyle \{(1,1), (1,2), (2,3), (3,2)\}. The first component `1` is mapped to two different values: `1` and `2`. So it is not a function.
*Note: Option B is mathematically a valid function. The textbook key lists Option C (None of these) as correct, which is a typographical error.*
Hence, **Option B** is the correct answer.

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