Question

Which of the following relations do not represent a function?

• A. P and S
• B. R and S
• C. Q and R
• D. P and Q

Answer 1

The correct option is B R and S

Detailed step-by-step solution:
Let’s consider all the four relations given here.
We know,
1. If all the inputs are not engaged in a relation from $x$ to $y,$ then the relation does not qualify as a function.
2. Every input should be related to exactly one output. If that is not the case, then a relation will not qualify as a function.

Relation P: The input and output pairs are: $(-2,4),(-1,1),(0,0),(3,9)$
Here, each input has a unique output. And all the inputs from $x$ has relations to the outputs in $y.$
So, this relation satisfies the conditions of a function.


Relation Q: The input and output pairs are: $(-2,1),(-1,1),(0,0),(3,0)$
Here, each input has a unique output. And all the inputs from $x$ has relations to the outputs in $y.$
So, this relation satisfies the conditions of a function.


Relation R: The input and output pairs are: $(-2,1),(-1,0),(0,9)$
Here, the input $3$ is not mapped to any output in $y,$ i.e., all the inputs from $x$ do not have a relation to the output in $y.$
So, this relation does not satisfy the conditions of a function.

Relation S: The input and output pairs are: $(-2,4),(-2,1),(-1,0),(0,0),(3,9)$
Here, for the input of $-2,$ there exists more than one output, i.e., here, the input $-2$ does not have a unique output.
So, this relation does not satisfy the conditions of a function.

So, relations $R$ and $S$ both are not satisfying the conditions of a function.

So, option C is the correct answer.