FYUG Even Semester Exam, 2025
Philosophy: PHIDSM-251/252 (Logic)
UNIT-I
Question 1 (a) [2 Marks]
What is Logic?
Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning.
Question 1 (b) [2 Marks]
What are the different forms of simple proposition?
[span_5](start_span)In traditional logic, simple (categorical) propositions take four forms based on quality and quantity:
[span_5](end_span)- A: Universal Affirmative (All S is P)
- E: Universal Negative (No S is P)
- I: Particular Affirmative (Some S is P)
- O: Particular Negative (Some S is not P)
Question 2 (a) [10 Marks]
What is meant by 'Truth' and 'Validity' in Logic? Distinguish between them with suitable examples.
Truth: Truth is a property of individual propositions (statements). A statement is true if it corresponds to reality.
Validity: Validity is a property of deductive arguments. An argument is valid if its structure is such that if the premises are true, the conclusion must be true.
| Feature | Truth | Validity |
|---|---|---|
| Applied to | Single Statements | Arguments (Structure) |
| Example | "All humans are mortal" (True) | All A are B; All B are C; Therefore All A are C (Valid) |
Distinction: An argument can be valid even if its premises are false (e.g., All dogs are cats; All cats are birds; Therefore all dogs are birds). Conversely, a set of true statements does not automatically form a valid argument if the logic is disconnected.
UNIT-II
Question 3 (b) [2 Marks]
What is obversion?
Obversion is a type of immediate inference in which the quality of the subject-predicate relationship is changed and the predicate is replaced by its complement.
Question 4 (b) [10 Marks]
Discuss the traditional square of opposition. How does it differ from Boolean square?
Traditional Square: Defines the relationships between A, E, I, and O propositions:
- Contradictories: A and O; E and I (One must be true, one false).
- Contraries: A and E (Both cannot be true).
- Subcontraries: I and O (Both cannot be false).
- Subalternation: A to I; E to O (Truth flows down, falsity flows up).
Boolean Difference: George Boole argued that universal propositions (A and E) do not have existential import (they don't claim the subject exists). Consequently, in the Boolean square, only contradictory relationships remain valid; subalternation, contraries, and subcontraries are rejected.
UNIT-III
Question 5 (a) [2 Marks]
What is figure? How many figures are there in categorical syllogism?
The figure of a syllogism is determined by the position of the middle term (M) in the premises. There are four figures in total.
Question 6 (a) [10 Marks]
What is categorical syllogism? Explain the structure and state Copi's general rules.
Definition: A deductive argument consisting of three categorical propositions (two premises and one conclusion) containing exactly three terms.
Structure:
- Major Term (P): Predicate of the conclusion.
- Minor Term (S): Subject of the conclusion.
- Middle Term (M): Appears in both premises but not the conclusion.
Copi's Rules:
- A valid syllogism must contain exactly three terms used consistently.
- The middle term must be distributed in at least one premise.
- If a term is distributed in the conclusion, it must be distributed in the premise.
- No syllogism is valid if it has two negative premises.
- If one premise is negative, the conclusion must be negative.
UNIT-IV
Question 7 (c) [2 Marks]
What is tautology?
A tautology is a statement form that is true under all possible assignments of truth values to its components (e.g., p ∨ ~p).
Question 8 (b) [10 Marks]
Symbolize the following statements using capital letters:
- If Arun teases (A) then if Bandana shouts (B) then Chandana will be angry (C).
Symbol: A ⊃ (B ⊃ C) - Either Amita shouts (A) and Bimal teases (B) or it is not the case both that Champak goes outside (C) and Dipika cooks (D).
Symbol: (A · B) ∨ ~(C · D) - It is not the case that either Picklu gets the prize (P) or Biplu fails (B).
Symbol: ~(P ∨ B) - If Akash comes (A) then both Bikash (B) and Promesh (P) will go.
Symbol: A ⊃ (B · P)
UNIT-V
Question 10 (a) [10 Marks]
What is formal proof of validity? State nine rules of inference.
A formal proof of validity is a sequence of statements, each of which is either a premise or follows from preceding statements by a rule of inference, ending with the conclusion.
Nine Rules of Inference (Examples):
- Modus Ponens (M.P.): p ⊃ q; p; ∴ q
- Modus Tollens (M.T.): p ⊃ q; ~q; ∴ ~p
- Hypothetical Syllogism (H.S.): p ⊃ q; q ⊃ r; ∴ p ⊃ r
- Disjunctive Syllogism (D.S.): p ∨ q; ~p; [span_55](start_span)∴ q[span_55](end_span)
- Constructive Dilemma (C.D.): (p ⊃ q) · (r ⊃ s); p ∨ r; ∴ q ∨ s
- Simplification (Simp.): p · q; ∴ p
- Conjunction (Conj.): p; q; ∴ p · q
- Addition (Add.): p; ∴ p ∨ q
- Absorption (Abs.): p ⊃ q; ∴ p ⊃ (p · q)