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

Concept:
• A Relation from set A to B is any subset of the Cartesian product \(A \times B\).
• A Function is a special relation where every element in the domain (A) is mapped to exactly one element in the codomain (B).

Step 1: Evaluate Assertion (A)
By definition, a function is defined as a subset of a relation that satisfies the uniqueness condition. Therefore, mathematically, the set of all functions is a subset of the set of all relations. This makes (A) true.

Step 2: Evaluate Reason (R)
One of the primary rules of a function is that one input cannot have multiple different outputs. A relation can be "one-to-many", but if it is, it fails to be a function. Functions must be either "one-to-one" or "many-to-one". Thus, (R) is false.