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Logic Exercises: Deriving Conclusions from Premises - Prof. Cowan, Exercises of Introduction to Philosophy

Introduction to Logic. Logic is the study of the criteria used in evaluating inferences or arguments. An inference is a process of reasoning in which a new belief is formed on the basis of or in virtue of evidence or proof supposedly provided by other beliefs.

Typology: Exercises

2020/2021

Available from 01/09/2023

Mahitab
Mahitab 🇺🇸

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Exercise 37 ... (For-Credit of 10 Points)
(based on Textbook Exercises, 4-2 & 4-5)
Derive the conclusions from the premises in the arguments below
by utilizing inference rules:
======================================
[37-1]
C: G
---------------------
1: ~M Premise
2: N -> G Premise
3: N v M Premise
4:N Disjunctive syllogism
5:G Modus ponens
G being derived from the above premises
======================================
[37-2]
C: D
-----------------------
1: ~G -> (A v B) Premise
2: ~B Premise
3: A -> D Premise
4: ~G Premise
5:A v B 1,4 modus ponens
6:A 2,5 Disjunctive syllogism
7:D 3,6 Modus ponens
D Derived from above premises
======================================
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Exercise 37 ... (For-Credit of 10 Points) (based on Textbook Exercises, 4-2 & 4-5) Derive the conclusions from the premises in the arguments below by utilizing inference rules: ====================================== [37-1] C: G


1: ~M Premise 2: N -> G Premise 3: N v M Premise 4:N Disjunctive syllogism 5:G Modus ponens G being derived from the above premises ====================================== [37-2] C: D


1: ~G -> (A v B) Premise 2: ~B Premise 3: A -> D Premise 4: ~G Premise 5:A v B 1,4 modus ponens 6:A 2,5 Disjunctive syllogism 7:D 3,6 Modus ponens D Derived from above premises ======================================

[37-3]

C: ~B

1: A -> (B -> C) Premise 2: ~C Premise 3: ~D -> A Premise 4: C V ~D Premise 5: ~D 2,4 disjunctive syllogism 6:A 3,5 Modus ponens 7:B -> C 1,6 modus ponens 8: ~B 2,7 Modus tollens ~B derived from above premises ====================================== [37-4] C: D & E


1: A -> (~B & C) Premise 2: C -> D Premise 3: E v B Premise 4: A Premise 5:~B & C 1,4 modus ponens 6:c rule of conjunction 7:~B 5, rule of conjunction 8:D 2,6 modus ponens 9:E 3,7 Disjunctive syllogism 10:D & E 8,9 rule of conjunction D & E derived from above premise ====================================== [37-5] C: ~F


1: (F -> G) v H premise