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Let Vbe the set of binary strings that is defined recursively as follows: I Base: 1 e V II Recursion: If s e Vthen also ) s0 E V (b) Os e V (c) 1sl e V. III Restriction: No object is an element of Vunless compelled so by I and/or II. It is straightforward to prove, using structural induction, that every string in V contains an odd number of l's. Prove the opposite: every binary string that contains an odd number of 1's, is an element of V.

Let Vbe the set of binary strings that is defined recursively as follows: I Base: 1 e V II Recursion: If s e Vthen also ) s0 E V (b) Os e V (c) 1sl e V. III Restriction: No object is an element of Vunless compelled so by I and/or II. It is straightforward to prove, using structural induction, that every string in V contains an odd number of l's. Prove the opposite: every binary string that contains an odd number of 1's, is an element of V.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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AA Let Vbe the set of binary strings that is defined recursively as follows: 6. I Base: 1 € V II Recursion: If s e Vthen also (а) s0 € V (b) Os e V (c) 1sl e V. III Restriction: No object is an element of Vunless compelled so by I and/or II. It is straightforward to prove, using structural induction, that every string in V contains an odd number of l's. Prove the opposite: every binary string that contains an odd number of 1's, is an element of V. (The following is one way to do this. For k > 0, let Bị be the set of all binary strings that contain exactly 2k + 1 1's. Then use the principle of weak mathematical induction to prove that BC V for each k.) ייון
Transcribed Image Text:AA Let Vbe the set of binary strings that is defined recursively as follows: 6. I Base: 1 € V II Recursion: If s e Vthen also (а) s0 € V (b) Os e V (c) 1sl e V. III Restriction: No object is an element of Vunless compelled so by I and/or II. It is straightforward to prove, using structural induction, that every string in V contains an odd number of l's. Prove the opposite: every binary string that contains an odd number of 1's, is an element of V. (The following is one way to do this. For k > 0, let Bị be the set of all binary strings that contain exactly 2k + 1 1's. Then use the principle of weak mathematical induction to prove that BC V for each k.) ייון
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