If a relation R on the set of natural numbers | vedclass

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Question

(A) The relation $R$ is defined on the set of natural numbers $N = \{1, 2, 3, \dots\}$ by the equation $x + 2y = 8$.We can rewrite this as $x = 8 - 2y

Vedclass · Accepted Answer

$\{2, 4, 6\}$

Vedclass · Answer

(A) The relation $R$ is defined on the set of natural numbers $N = \{1, 2, 3, \dots\}$ by the equation $x + 2y = 8$.We can rewrite this as $x = 8 - 2y$.Since $x \in N$,we must have $x > 0$,which implies $8 - 2y > 0$,so $2y Since $y \in N$,the possible values for $y$ are $1, 2, 3$.Now,we find the corresponding values of $x$ for each $y$:If $y = 1$,$x = 8 - 2(1) = 6$.If $y = 2$,$x = 8 - 2(2) = 4$.If $y = 3$,$x = 8 - 2(3) = 2$.Thus,the relation $R$ is the set of ordered pairs: $R = \{(6, 1), (4, 2), (2, 3)\}$.The domain of $R$ is the set of all first elements of the ordered pairs in $R$.Therefore,the domain is $\{2, 4, 6\}$.

If a relation $R$ on the set of natural numbers $N$ is defined by $x + 2y = 8$,then the domain of $R$ is:

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