Given the premises a → b , d, d → b and a, consider the following proof of b: 1. a Premise 2. a b Premise. 3. b Modus Ponens 1, 2 The argument is not valid; it doesn't use all the premises O valid not valid because using d and d → b also can be used to derive b, and it is preferable to use the premises first listed. ridiculous O not välid; the shortest possible proof is 4 lines long.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 10TFE
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Q10 Please provide correct answer with justification asap
Question 10
Given the premises a → b, d, d b and a, consider the following proof of b:
1. а
Premise
2. a b Premise.
3. Ь
Modus Ponens 1, 2
The argument is
O not valid; it doesn't use all the premises
valid
not valid because using d and d → b also can be used to derive b, and it is preferable to use the premises fırst listed.
ridiculous
O not välid; the shortest possible proof is 4 lines long.
Transcribed Image Text:Question 10 Given the premises a → b, d, d b and a, consider the following proof of b: 1. а Premise 2. a b Premise. 3. Ь Modus Ponens 1, 2 The argument is O not valid; it doesn't use all the premises valid not valid because using d and d → b also can be used to derive b, and it is preferable to use the premises fırst listed. ridiculous O not välid; the shortest possible proof is 4 lines long.
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