Question

Define a relation $R$ on the set $N$ of natural number by $R=$ {$(x,y):y=x+5,x\text{is a natural number less than}4;x,yϵN$}. Depict this relationship using roster form. Write down the domain and the range.

Answer 1

Given
$R=$ {$(x,y);y=x+5,x<4;x,yϵN$}

Finding Roster form
Natural numbers less than $4$ are $1,2,3$
Put $x=1,2,3$ in $y=x+5$ and we get $y=6,7,8$ respectively.
So, $R=$ {$(1,6),(2,7),(3,8)$}

Domain of $R$
The domain of $R$ is the set of all first elements of ordered pairs in relation $R$.
Hence, domain of $R=$ {$1,2,3$}

Range of $R$
The range of $R$ is set of second elements of ordered pairs in relation $R$.
Hence, range of $R=$ {$6,7,8$}