Phil 109: Introduction to Formal Reasoning and Decision Making

This assignment solution for Phil 109: Introduction to Formal Reasoning and Decision Making covers various aspects of formal logic and argument analysis. Part 1 focuses on identifying argument types (deductive and inductive) and the specific types of arguments presented. Part 2 delves into the validity of deductive arguments, providing counterexamples where necessary to demonstrate invalid forms. Part 3 involves symbolic representation of arguments using propositional logic, including the use of symbols and operators, and determining the validity of complex arguments. Part 4 explores propositional logic further, including the use of truth tables to determine the properties of logical statements, such as self-contradictory, tautologous, and contingent statements, and to assess the consistency or inconsistency of sets of statements. The solution provides detailed answers and explanations for each question, demonstrating a solid understanding of formal reasoning principles.

FORMAL REASONING AND DECISION MAKING
FORMAL REASONING AND DECISION MAKING
Name of the Student
Name of the University
Author note

1FORMAL REASONING AND DECISION MAKING
Part 1: 1.1
Answer 1: Deductive, argument based on definition.
Answer 2: Deductive, conditional argument- Modus Tolens.
Answer 3: Inductive, argument based on authority.
Answer 4: Inductive, predictive argument.
Answer 5: Inductive, argument based on analogy.
Part 1: 1.2
Answer 6: Deductive, valid.
Answer 7: Deductive, invalid.
Answer 8: Deductive, invalid.
Answer 9: Inductive, weak.
Answer 10: Inductive, strong.
Part 2: 2.1
Answer 11:
Form – All A are B, so all B are A.
Counter example – All footballers are sportspersons. Therefore, all sportspersons are footballers.
(It is invalid because being a sportsperson does not specifically mean that they are footballers).
Answer 12:
Form – All A’s are B’s. Since all A’s are C’s. All B’s are C’s.

2FORMAL REASONING AND DECISION MAKING
Counter example – It follows that all mangoes are fruits, since all mangoes are plants and all
fruits are plants.
Answer 13:
Form – Either A or B. It is A, so not B.
Counter example – Either I will go for cycling or I will go to a concert. I went for cycling. So, I
did not go to the concert. (It is invalid because going cycling does not entail not going to the
concert).
Answer 14:
Form – If A is B, then A is C. A is C, so A is B.
Counter example – If a polygon has four sides, then it is a square. A polygon is a square. So, a
polygon has four sides. (It is invalid because being a polygon does not mean that it will be a
square).
Answer 15:
Form – If A is B, then A is C and if A is B, then A is D. So, if A is C, then A is D.
Counter example – If he listens to music, then he listens to Eminem; and if he listens to music,
then he listens to rap music. So, if he listens to Eminem, then he listens to rap music. (It is
invalid because listening to music does not necessarily mean listening to rap music).
Part 2: 2.2
Answer 16:
Valid, Modus Tolens.

3FORMAL REASONING AND DECISION MAKING
Answer 17:
Valid, pure hypothetical syllogism.
Answer 18:
Valid, disjunctive syllogism.
Answer 19:
Valid, Modus Tolens.
Answer 20:
Valid, general categorical syllogism.
Part 3: 3.1
Answer 21: D → B ^C
Answer 22: N ^ E; N→ G
Answer 23: M ∧ C
Answer 24: W∧ L ≡ E
Answer 25: L ≡ H, L ≡ S
Part 3: 3.2
Answer 26:
S → F → P
Valid, Modus Ponens.

4FORMAL REASONING AND DECISION MAKING
Answer 27:
S ∧ M → P
Valid, pure hypothetical syllogism.
Answer 28:
M → L → H
Valid, modus ponens.
Answer 29:
S → P ≡ A ∧ S
Counter example – Because
Answer 30:
D → E
Valid, argument based on mathematics.
Part 4: 4.1
Answer 31: ¬(¬M ∧ ¬N) → (M ∨ N) is self-contradictory.
Answer 32: [(J → L) ∧ (¬K → L)] ∧ ¬(L ∨ J) is tautologous.
Answer 33: [(A → B) ≡ (C ∧ D)] ∧ [(C → B) ≡ (A ∧ D)] is contingent.
Part 4: 4.2
Answer 34: (P ∧ Q) ∨ P with (P ∨ Q) ∧ Q is consistent.

5FORMAL REASONING AND DECISION MAKING
Answer 35: [(S → W) → X] with [(S ∧ W) ∨ (W ∧ X)] is contradictory.
Answer 36: P1 A → D
P2 ¬B ∨ A
P3 ¬(C ∨ D) is invalid.