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Prove the argument(∀x)[(B(x) ∨ C(x)) → A(x)] → (∀x)[B(x) → A(x)]

Prove the argument(∀x)[(B(x) ∨ C(x)) → A(x)] → (∀x)[B(x) → A(x)]

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Prove the argument
(∀x)[(B(x) ∨ C(x)) → A(x)] → (∀x)[B(x) → A(x)]

Expert Solution
Step 1

Given argument,

(∀x)​[(B(x) V C(x)) → A(x)] → (∀x)​[B(x) → A(x)]

Step 2

Answer:-

The proof sequence is as follows:-

1.(∀x)​[(B(x) V C(x)) → A(x)]             Hypothesis

2.(B(x) V C(x)) → A(x)                      Universal Instantiation

3.B(x)                                               Temporary Hypothesis

 

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