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Define a function B: N x N → N using the following recursive definition. B(0, n) n2 n>0, %3D В т, 0) В т - 1,1) m > 0, В т, п) В(т - 1, В(т, п —- 1)) т, п > 0. (a) Compute B(1, 1) . Show your working. (b) Compute B(2, 2) . Show your working. (c) Prove or disprove: for all r, y E N, B(r,y) = 1. 2.

Define a function B: N x N → N using the following recursive definition. B(0, n) n2 n>0, %3D В т, 0) В т - 1,1) m > 0, В т, п) В(т - 1, В(т, п —- 1)) т, п > 0. (a) Compute B(1, 1) . Show your working. (b) Compute B(2, 2) . Show your working. (c) Prove or disprove: for all r, y E N, B(r,y) = 1. 2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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2. Define a function B: N x N N using the following recursive definition. B(0, n) n2 n>0, B(m, 0) В(т - 1,1) m > 0, B(m, n) В (т — 1, B(т, п- 1)) т, п > 0. (a) Compute B(1, 1) . Show your working. (b) Compute B(2, 2) . Show your working. (c) Prove or disprove: for all r, y E N, B(r,y) = 1.
Transcribed Image Text:2. Define a function B: N x N N using the following recursive definition. B(0, n) n2 n>0, B(m, 0) В(т - 1,1) m > 0, B(m, n) В (т — 1, B(т, п- 1)) т, п > 0. (a) Compute B(1, 1) . Show your working. (b) Compute B(2, 2) . Show your working. (c) Prove or disprove: for all r, y E N, B(r,y) = 1.
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