Question

Let $R$ be a relation in the set of natural numbers defined by $R=\left\{\overline{)\left(1+x,1+x^2\right)}x<5,x\in N\right\}$ which of the following is false?

• A. $R=\left\{\left(2,2\right),\left(3,5\right),\left(4,10\right),\left(5,17\right),\left(6,25\right)\right\}$
• B. Domain of $R=\left\{2,3,4,5,6\right\}$
• C. Range of $R=\left\{2,5,10,17,26\right\}$
• D. (B) and (C) are true

Answer 1

The correct option is A

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

Determine the false statement

Given $R$ is a relation in the set and $R=\left\{\overline{)\left(1+x,1+x^2\right)}x<5,x\in N\right\}$

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

Then the domain is listed as $R=\left\{2,3,4,5,6\right\}$ and the range is listed as $R=\left\{2,5,10,17,26\right\}$

Therefore, option A is a false statement.