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8. We know that P₁= P2 on B3 if P₁ = P2 on C, provided that C generates B and is a 7-system. Show this last property cannot be omitted. For example, consider 2 (a, b, c, d) with = 1 P₁({a})= P₁({d})= P₂({b})= P₂({c})= and 1 P₁{{b}) = P₁({c}) = P₂{{a}}) = P2({d}) = 3. Set C= {(a, b), (d, c), (a, c}, {b, d}}.

8. We know that P₁= P2 on B3 if P₁ = P2 on C, provided that C generates B and is a 7-system. Show this last property cannot be omitted. For example, consider 2 (a, b, c, d) with = 1 P₁({a})= P₁({d})= P₂({b})= P₂({c})= and 1 P₁{{b}) = P₁({c}) = P₂{{a}}) = P2({d}) = 3. Set C= {(a, b), (d, c), (a, c}, {b, d}}.

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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8. We know that P₁= P2 on B3 if P₁ = P2 on C, provided that C generates B and is a 7-system. Show this last property cannot be omitted. For example, consider 2 (a, b, c, d) with = 1 P₁({a})= P₁({d})= P₂({b})= P₂({c})= and 1 P₁({b}) = P₁({c}) = P₂{{a}} = P2({d}) = 3. Set C = {(a, b), (d, c), {a, c}, {b, d}}.
Transcribed Image Text:8. We know that P₁= P2 on B3 if P₁ = P2 on C, provided that C generates B and is a 7-system. Show this last property cannot be omitted. For example, consider 2 (a, b, c, d) with = 1 P₁({a})= P₁({d})= P₂({b})= P₂({c})= and 1 P₁({b}) = P₁({c}) = P₂{{a}} = P2({d}) = 3. Set C = {(a, b), (d, c), {a, c}, {b, d}}.
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