Question

To determine list of the ordered pairs in the relation $R$from $A=\{0,1,2,3,4\}$to $B=\{0,1,2,3\}$, where $(a,b)\in R$if and only if $lcm(a,b)=2$.

Short answer

$R=\left\{\right(1,2),(2,1\left)\right\}$

Step-by-step solution

Given data

$A=\{0,1,2,3,4\}$ and $B=\{0,1,2,3\}$

Concept used ordered pair

An ordered pair $\mathbf{(}\mathit{a}\mathbf{,}\mathit{b}\mathbf{)}$is a pair of elements associated in such a way that order matters. That is, the ordered pair $\mathbf{(}\mathit{a}\mathbf{,}\mathit{b}\mathbf{)}$is different from $\mathbf{(}\mathit{b}\mathbf{,}\mathit{a}\mathbf{)}$unless$\mathbf{\text{a}}\mathbf{=}\mathbf{\text{b}}$.

Solve for relation

Ordered pairs are formed from set A and B.

$R=\left\{\right(1,2),(2,1\left)\right\}$