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Reptile [31]
2 years ago
9

Consider the recursively defined set S: Basis Step: The unit circle is in S. Recursive Step: if x is in S, then x with a line th

rough any diameter is in S. (a) (4 points) Prove that: is in S. (b) ( 6 points) For an element x ∈ S, define V (x) be the number of vertices (i.e. the number of intersections of lines and arcs and lines with lines), let E(x) to be the number of edges (line segments or arcs between vertices), and let F(x) be the number of faces. Prove that for any x ∈ S that F + V = E + 1. (Please use structural induction.)

Mathematics
1 answer:
Schach [20]2 years ago
7 0

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images for the step by step explanation to the question

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