Question

Given below are two statements :
one is labelled as
Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) :
Every function is a relation.
Reason (R) :
A function can be one to many.
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Function Test: One input $\to$ One output. If you see "one-to-many," it's just a general relation, like a person having multiple phone numbers.

Answer 1

The Correct Option is C

In discrete mathematics, there are strict definitions for relations and functions. 1. Analyzing Assertion (A): A relation is defined as any subset of the Cartesian product of two sets. A function is a specific type of relation where every element of the domain is associated with exactly one element of the codomain. Since a function is a subset of a relation that follows stricter rules, every function is inherently a relation. Thus, Assertion (A) is correct. 2. Analyzing Reason (R): The fundamental property of a function is that it must be "well-defined," meaning one input cannot map to multiple different outputs. If an input $x$ maps to both $y_1$ and $y_2$, it is a relation but not a function. Therefore, a function cannot be one-to-many. It must be one-to-one or many-to-one. Thus, Reason (R) is incorrect. 3. Conclusion: The assertion is a basic truth of set theory, but the reason provides a definition that actually disqualifies a mapping from being a function.