The formulas A →(B ∧C) and (A →B) ∧(A →C) are logically equivalent. For this problem, you are going to prove that they are equivalent in two different ways. (a) Prove that A →(B ∧C) ≡ (A →B) ∧(A →C) by writing two natural deduction proofs: one proving A → (B ∧ C) ⊢ (A → B) ∧ (A → C) and another proving (A→B) ∧(A→C) ⊢A→(B ∧C) (using only the eight natural deduction inference rules and no equivalence rules). (b) Prove that A →(B ∧C) ≡(A →B) ∧(A →C) by writing an equivalence proof.
The formulas A →(B ∧C) and (A →B) ∧(A →C) are logically equivalent. For this problem, you are going to prove that they are equivalent in two different ways. (a) Prove that A →(B ∧C) ≡ (A →B) ∧(A →C) by writing two natural deduction proofs: one proving A → (B ∧ C) ⊢ (A → B) ∧ (A → C) and another proving (A→B) ∧(A→C) ⊢A→(B ∧C) (using only the eight natural deduction inference rules and no equivalence rules). (b) Prove that A →(B ∧C) ≡(A →B) ∧(A →C) by writing an equivalence proof.
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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The formulas A →(B ∧C) and (A →B) ∧(A →C) are logically equivalent. For this
problem, you are going to prove that they are equivalent in two different ways.
(a) Prove that A →(B ∧C) ≡ (A →B) ∧(A →C) by writing two natural deduction
proofs: one proving A → (B ∧ C) ⊢ (A → B) ∧ (A → C) and another proving
(A→B) ∧(A→C) ⊢A→(B ∧C) (using only the eight natural deduction inference
rules and no equivalence rules).
(b) Prove that A →(B ∧C) ≡(A →B) ∧(A →C) by writing an equivalence proof.
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