Let R  be a relation in N defined by R=1+x,1+x2:x≤5,x∈N.Which of the following is false?

# Let $R$  be a relation in $N$ defined by $R=\left\{\left(1+x,1+{x}^{2}\right):x\le 5,x\in N\right\}$.Which of the following is false?

1. A

$R=\left\{\left(2,2\right),\left(3,5\right),\left(4,10\right),\left(5,17\right),\left(6,25\right)\right\}$

2. B

Domain of $R=\left\{2,3,4,5,6\right\}$

3. C

Range of $R=\left\{2,5,10,17,26\right\}$

4. D

None of these

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### Solution:

$R=\left\{\left(2,2\right),\left(3,5\right),\left(4,10\right),\left(5,17\right),\left(6,26\right)\right\}$

Domain of $R=\left\{x:\left(x,y\right)\in N\right\}=\left\{2,3,4,5,6\right\}$

and range of $R=\left\{y:\left(x,y\right)\in N\right\}=\left\{2,5,10,17,26\right\}$

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