A relation defined from A -0-1-2-3-4 to N as xRy iff x - y- Then which among the following options is correctA- R -1 is a function with range as AB- R is a function with range as NC- R is a function with range as 1-2-3-4D- R is not a function

The correct option is D R is not a functionHere R = { (1,1),(2,2),(3,3),(4,4) } As 0 ∈ A but doesn't have any image in ℕ So, it is not a function HereR^ 1= { ...

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Standard XII

Mathematics

Definition of Function

A relation de...

Question

A relation defined from $A = {0, 1, 2, 3, 4}$ to $N$ as $x R y iff x = y$ . Then which among the following options is correct

R^{- 1}

is a function with range as

A

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R

is a function with range as

N

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R

is a function with range as

{1, 2, 3, 4}

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R

is not a function

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Solution

The correct option is D $R$ is not a function
Here $R = {(1, 1), (2, 2), (3, 3), (4, 4)}$
As $0 \in A$ but doesn't have any image in $N$
So, it is not a function

Here $R^{- 1} = {(1, 1), (2, 2), (3, 3), (4, 4)}$
As $5 \in N$ but doesn't have any image in $A$
So, it is not a function

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Definition of Function

Standard XII Mathematics

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A relation defined from A={0,1,2,3,4} to N as xRy iff x=y. Then which among the following options is correct

The correct option is D R is not a functionHere R={(1,1),(2,2),(3,3),(4,4)} As 0∈A but doesn't have any image in N So, it is not a function HereR−1={(1,1),(2,2),(3,3),(4,4)} As 5∈N but doesn't have any image in A So, it is not a function

A relation defined from $A = {0, 1, 2, 3, 4}$ to $N$ as $x R y iff x = y$ . Then which among the following options is correct

The correct option is D $R$ is not a function
Here $R = {(1, 1), (2, 2), (3, 3), (4, 4)}$
As $0 \in A$ but doesn't have any image in $N$
So, it is not a function

Here $R^{- 1} = {(1, 1), (2, 2), (3, 3), (4, 4)}$
As $5 \in N$ but doesn't have any image in $A$
So, it is not a function