Rule 7.2.9: Implication a. Vr (C → A(x)) = C → Vx A(x) b. 3x (C → A(x)) = C → 3x A(x) c. Vx (A(x) → C) = 3x A(x) –→ C d. Эx (A(г) —> C) %3D Vx A(z) — С

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 6AEXP
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Consider the equivalence rule 7.2.9c. Note that x does not occur free in C in this equivalence.
Prove 7.2.9c using other equivalences. That is, start with the left-hand-side of 7.2.9c, and use other
equivalences to transform the left hand side to equivalent formulas until you obtain the right-handside of 7.2.9c (or start with the right-hand-side and obtain the left-hand-side). Write down your
work step by step very clearly, stating which equivalence you are using for each step.

Rule 7.2.9: Implication
a. Vr (C → A(x)) = C → Vx A(x)
b. 3x (C → A(x)) = C → 3x A(x)
c. Vx (A(x) → C) = 3x A(x) –→ C
d. Эx (A(г) —> C) %3D Vx A(z) — С
Transcribed Image Text:Rule 7.2.9: Implication a. Vr (C → A(x)) = C → Vx A(x) b. 3x (C → A(x)) = C → 3x A(x) c. Vx (A(x) → C) = 3x A(x) –→ C d. Эx (A(г) —> C) %3D Vx A(z) — С
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