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Given the relation V, use ordered pair notation to express the relation

V∘V.

Option a:
(x,x)
Option b:
(y,y)
Option c:
(x,y)
Option d:
(y,x)

User Selima
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1 Answer

1 vote

Final answer:

The composition of the relation V with itself (V∘V) implies applying the relation twice, starting with an input x and seeking an output that matches the original input x, yielding ordered pairs (x,x). This corresponds to Option a.

Step-by-step explanation:

To determine the notation for the composition of the relation V with itself (indicated as V∘V), we require a closer look into the nature of the relation V and how compositions of relations work. Given the information and the context of a mathematical function described as a linear equation of the form y = b + mx, we can infer that the variables x and y represent the domain and range of the relation V, respectively.

When a relation is composed with itself (e.g., V∘V), we are looking for an output that matches the original input after applying the relation twice. Therefore, if we start with an input x and apply V, we get an output y. If we then apply V again to the y we've just obtained (considering this y as a new input), we would typically get another value. However, since we are looking for the composition of V with itself, we are interested in the scenario where the output of the second application matches the input of the first. Thus, the resulting ordered pairs from V∘V would start with x and end with x, assuming the composition leads to the original input value.

Based on this understanding, the correct notation for the composition of relation V with itself would be (x,x), which matches Option a.

User Flamey
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