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Q2 Formal Induction We know that the Distributive Law tells us that a ^ (B₁ V B₂) = (a ^ B₁) V (α ^ B₂), for any propositions a, 3₁, and 32. Suppose that VB; denotes the n-term disjunction, B₁ V B₂ V ... V B₁. i=1 Thus, the two-term Distributive Law could have been rewritten as: 2 2 a^V Bi= V(a^ Bi). i=1 i=1 Use formal mathematical induction as well as the two-term version of the Distributive Law to prove the generalization of the Distributive Law to n terms: n 12 a^V Bi = V(a ^ Bi), for all integers n > 2. i=1 i=1

Q2 Formal Induction We know that the Distributive Law tells us that a ^ (B₁ V B₂) = (a ^ B₁) V (α ^ B₂), for any propositions a, 3₁, and 32. Suppose that VB; denotes the n-term disjunction, B₁ V B₂ V ... V B₁. i=1 Thus, the two-term Distributive Law could have been rewritten as: 2 2 a^V Bi= V(a^ Bi). i=1 i=1 Use formal mathematical induction as well as the two-term version of the Distributive Law to prove the generalization of the Distributive Law to n terms: n 12 a^V Bi = V(a ^ Bi), for all integers n > 2. i=1 i=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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Q2 Formal Induction We know that the Distributive Law tells us that a ^ (3₁ V 3₂) = (a ^ B₁) V (a^ B₂), for any n propositions a, 3₁, and 32. Suppose that V Bi denotes the n-term disjunction, 3₁ V 3₂ V ... V B₁. i=1 Thus, the two-term Distributive Law could have been rewritten as: 2 2 α ^ V Bi = V(α ^ Bi). i=1 i=1 Use formal mathematical induction as well as the two-term version of the Distributive Law to prove the generalization of the Distributive Law to n terms: n 72 a^V Bi = V(a ^ Bi), for all integers n > 2. i=1 i=1
Transcribed Image Text:Q2 Formal Induction We know that the Distributive Law tells us that a ^ (3₁ V 3₂) = (a ^ B₁) V (a^ B₂), for any n propositions a, 3₁, and 32. Suppose that V Bi denotes the n-term disjunction, 3₁ V 3₂ V ... V B₁. i=1 Thus, the two-term Distributive Law could have been rewritten as: 2 2 α ^ V Bi = V(α ^ Bi). i=1 i=1 Use formal mathematical induction as well as the two-term version of the Distributive Law to prove the generalization of the Distributive Law to n terms: n 72 a^V Bi = V(a ^ Bi), for all integers n > 2. i=1 i=1
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