FYUG Even Semester Exam, 2025
Philosophy: PHIDSM-251/252 (Logic)

4th Semester | Full Marks: 70 | Pass Marks: 28 | Time: 3 Hours

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:

  1. Major Term (P): Predicate of the conclusion.
  2. Minor Term (S): Subject of the conclusion.
  3. 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:

  1. If Arun teases (A) then if Bandana shouts (B) then Chandana will be angry (C).
    Symbol: A ⊃ (B ⊃ C)
  2. 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)
  3. It is not the case that either Picklu gets the prize (P) or Biplu fails (B).
    Symbol: ~(P ∨ B)
  4. 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)