Question

Which of the following statements is correct-

• A. All Relations are Functions
• B. All Functions are Relations
• C. Some Functions are NOT Relations
• D. Some Relations are NOT Functions

Answer 1

Answer: (B), (D)

Some Relations are NOT Functions

Assume: Relation $R:A\to B$
Concept: For a relation to be a function, all elements of set $A$ must be mapped with exacly one element of set $B$.

Hence, all functions are relations but all relations are not functions.

For example,
$R:X\to Y$

Here, elements $2\&6$ in set $X$ are mapped with more than one elements in set $Y$, hence it is a relation from set $X$ to set $Y$ but it is not a function.

And example of relation which is function is given in below
$R:X\to Y$

Here, each element of set X is mapped with exactly one element of set Y, hence given relation is a function.