Recursive Step: If ax ES, then bax ES and cax E S. S, then cbx € S. S, then bax ES and bcx E S. S, then ddx E S. Closure: SE S only if it is a, b or c or it can be obtained from a, b or c using operations of the Recursive Step. If bx If cx If dx a) What recursive step can be removed from the above definition and v b) Derive from the definition of S that bcbc S. c) Explain why baa & S.
Recursive Step: If ax ES, then bax ES and cax E S. S, then cbx € S. S, then bax ES and bcx E S. S, then ddx E S. Closure: SE S only if it is a, b or c or it can be obtained from a, b or c using operations of the Recursive Step. If bx If cx If dx a) What recursive step can be removed from the above definition and v b) Derive from the definition of S that bcbc S. c) Explain why baa & S.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
Transcribed Image Text:The following recursive definition of a set S over {a, b, c, d}.
Basis: "", a, b, c E S.
Recursive Step: If ax E S, then bax ES and cax E S.
If bx € S, then cbx € S.
If cx = S, then bax ES and bcx = S.
If dx E S, then ddx E S.
Closure: SE S only if it is a, b or c or it can be obtained from a, b or c using finitely many
operations of the Recursive Step.
a) What recursive step can be removed from the above definition and why?
b) Derive from the definition of S that bcbc S.
c) Explain why baa & S.
Expert Solution
Step 1: given question
Consider the following recursive definition of a set S over {a, b, c, d}.
Basis: “”, a, b, c ∈ S.
Recursive Step: If ax ∈S, then bax ∈ S and cax ∈ S.
If bx ∈ S, then cbx ∈ S.
If cx ∈ S, then acx ∈ S and bcx ∈ S.
If dx ∈ S, then ddx ∈ S.
Closure: s ∈ S only if it is a, b or c or it can be obtained from a, b or c using finitely many operations of the Recursive Step.
- What recursive step can be removed from the above definition and why?
- Derive from the definition of S that bcbc ∈ S.
- Explain why baa ∉ S.
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