et S be the subset of the set of ordered pairs of integers defined recursively by Basis step: (0,0) E S Recursive step: If (a, b) E S, then (a, b + 1) E S, (a + 1, b + 1) E S, and (a + 2, b+1) Є S. Use structural induction to show that a ≤ 2b whenever (a, b) E S.Which statements are required to show the recursive step? (Check all that apply.) C NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let S be the subset of the set of ordered pairs of Integers defined recursively by Basis step: (0,0) € 5 Recursive step: If (a, b) e S, then (a, b+1)€ 5, (a+1, b+1)e S, and (a+2, b+1) S. Use structural induction to show that as 2b whenever (a, b) S. Which statements are required to show the recursive step? (Check all that apply.) Check All That Apply Suppose (a, b) satisfies as 2b. If (a, b) S and a≤ 2b, then adding the inequality 0 ≤2 gives a ≤ 2(b+1). If (a, b) Sand as 2b, then adding the inequality 12 gives a+1s2b+1). If (a, b) e Sand as 2b, then adding the inequality 2 ≤ 2 gives a + 2 ≤ 2(b+1). If (a, b) Sand a≤ 2b, then adding the inequality 0 ≤ 1 gives a≤ 2b+1.
et S be the subset of the set of ordered pairs of integers defined recursively by Basis step: (0,0) E S Recursive step: If (a, b) E S, then (a, b + 1) E S, (a + 1, b + 1) E S, and (a + 2, b+1) Є S. Use structural induction to show that a ≤ 2b whenever (a, b) E S.Which statements are required to show the recursive step? (Check all that apply.) C NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let S be the subset of the set of ordered pairs of Integers defined recursively by Basis step: (0,0) € 5 Recursive step: If (a, b) e S, then (a, b+1)€ 5, (a+1, b+1)e S, and (a+2, b+1) S. Use structural induction to show that as 2b whenever (a, b) S. Which statements are required to show the recursive step? (Check all that apply.) Check All That Apply Suppose (a, b) satisfies as 2b. If (a, b) S and a≤ 2b, then adding the inequality 0 ≤2 gives a ≤ 2(b+1). If (a, b) Sand as 2b, then adding the inequality 12 gives a+1s2b+1). If (a, b) e Sand as 2b, then adding the inequality 2 ≤ 2 gives a + 2 ≤ 2(b+1). If (a, b) Sand a≤ 2b, then adding the inequality 0 ≤ 1 gives a≤ 2b+1.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter3: Solving Equation And Problems
Section3.8: Proof In Algebra
Problem 6WE
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Transcribed Image Text:et S be the subset of the set of ordered pairs of integers defined recursively by
Basis step: (0,0) E S
Recursive step: If (a, b) E S, then (a, b + 1) E S, (a + 1, b + 1) E S, and (a + 2, b+1) Є S.
Use structural induction to show that a ≤ 2b whenever (a, b) E S.Which statements are
required to show the recursive step? (Check all that apply.)
C
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
Let S be the subset of the set of ordered pairs of Integers defined recursively by
Basis step: (0,0) € 5
Recursive step: If (a, b) e S, then (a, b+1)€ 5, (a+1, b+1)e S, and (a+2, b+1) S.
Use structural induction to show that as 2b whenever (a, b) S.
Which statements are required to show the recursive step? (Check all that apply.)
Check All That Apply
Suppose (a, b) satisfies as 2b.
If (a, b) S and a≤ 2b, then adding the inequality 0 ≤2 gives a ≤ 2(b+1).
If (a, b) Sand as 2b, then adding the inequality 12 gives a+1s2b+1).
If (a, b) e Sand as 2b, then adding the inequality 2 ≤ 2 gives a + 2 ≤ 2(b+1).
If (a, b) Sand a≤ 2b, then adding the inequality 0 ≤ 1 gives a≤ 2b+1.
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