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Let $A = \{3,4,5,6,7,8\}$ define a relation $R$ from $A$ to $A$ by,

$$R= \{(x,y) \,:\, y= x-1\}$$

what is the relation of $R$? and domain of $R$?

C.F.G
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Prabodya De Alwis
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    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Aug 26 '19 at 10:36
  • What do you mean by "what is the relation of R", when you have just previously defined the relation to be $$ R: \mathbb{N} \to \mathbb{N}\times \mathbb{N} : R = (x,x-1)~\text{with}~x \in A $$ ? – Matti P. Aug 26 '19 at 10:43
  • oki then can I know the domain and the range of the R? Domain= {3,4,5,6,7,8} and range is {2,3,4,5,6,7} is it correct? – Prabodya De Alwis Aug 26 '19 at 10:50

1 Answers1

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$R$ is the set of all ordered pairs of elements where each of which are elements of $A$ such that the first element is one larger than the second. If you want to write out all elements of $R$, that should be simple. Just write down all pairs of elements of $A$ such that the first element is one larger than the second.

Explicitly, $R$ would be $\{(4,3),(5,4),(6,5),(7,6),(8,7)\}$

Now... the domain is the set of all values that appear anywhere in the relation as the first element. The range is the set of all values that appear anywhere in the relation as the second element. In other words, the domain and the range are $\{4,5,6,7,8\}$ and $\{3,4,5,6,7\}$ respectively.

Note that $(3,2)$ is not an element of the relation because $2$ is not an element of $A$.

JMoravitz
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