UNIT-I
Question 1 [1 × 3 = 3 Marks]
(a) Is symbolic logic deductive in nature?
Yes, symbolic logic is primarily deductive in nature
.(b) Are 'Symbolic Logic' and 'Mathematical Logic' synonymous?
Yes, they are generally considered synonymous as both use mathematical symbols and methods to represent logical forms
.(c) What are Ideograms?
Ideograms are symbols that represent ideas or concepts directly rather than the sounds of words (e.g., symbols like ∨, ·, ⊃).
(d) What is the symbol of Negative Function/Negation?
The symbol is the Tilde (~) or sometimes a bar over the variable
.Question 2 [2 Marks]
State two characteristics of Symbolic Logic.
What are variables? What are constants?
Question 3 [5 Marks]
Option ASymbolize the following sentences using variables and logical constants:
(i) Asim is intelligent and honest: I · H (ii) Either India or Pakistan will win the match: I ∨ P (iii) If it rains, then there will be a good harvest: R ⊃ GUNIT-II
Question 4 [1 × 3 = 3 Marks]
(a) What is a statement form?
A statement form is a sequence of symbols containing statement variables such that when statements are substituted for the variables, the result is a statement
.(b) What is Tautology?
A tautology is a statement form that is true under all possible assignments of truth values to its variables
.(c) If p is true and q is false, then what will be the value of p ⊃ q?
The value will be False
.(d) When does an argument become invalid?
An argument is invalid if and only if it is possible for all its premises to be true while its conclusion is false
.Question 5 [2 Marks]
Draw the truth tables of the five basic truth functions.
| p | q | ~p | p · q | p ∨ q | p ⊃ q | p ≡ q |
|---|---|---|---|---|---|---|
| T | T | F | T | T | T | T |
| T | F | F | F | T | F | F |
| F | T | T | F | T | T | F |
| F | F | T | F | F | T | T |
Question 6 [5 Marks]
Use truth tables to characterize the following statement forms:
(i) p ⊃ (p ∨ q)
| p | q | p ∨ q | p ⊃ (p ∨ q) |
|---|---|---|---|
| T | T | T | T |
| T | F | T | T |
| F | T | T | T |
| F | F | F | T |
Result: Tautology (All T).
(ii) (p · q) · (p ∨ q)
| p | q | p · q | p ∨ q | (p · q) · (p ∨ q) |
|---|---|---|---|---|
| T | T | T | T | T |
| T | F | F | T | F |
| F | T | F | T | F |
| F | F | F | F | F |
Result: Contingent (Mixed T and F).
UNIT-III
Question 7 [1 × 3 = 3 Marks]
(a) Is shorter truth table method a decision procedure?
Yes, it is a decision procedure for testing validity
.(b) What is assumed in shorter truth table method?
We assume the argument is invalid by assigning True to premises and False to the conclusion to see if a contradiction arises
.(c) How many rows are required in shorter truth table method?
Only one row is required
.(d) "Indirect truth table method is also known as shorter truth-table method." Is it true?
Yes, it is true
.Question 9 [5 Marks]
Test the following argument forms using indirect truth table method:
(i) p ⊃ q, p / ∴ q
Assume Invalid: Premises (p ⊃ q)=T, p=T; Conclusion q=F.
Row: p=T, q=F. Then p ⊃ q becomes T ⊃ F = F. But premise was assumed T. Contradiction! Therefore, Valid.
UNIT-IV
Question 10 [1 × 3 = 3 Marks]
(a) State the rule of Modus Tollens (MT).
p ⊃ q, ~q / ∴ ~p
(d) State the rule of Addition (Add.).
p / ∴ p ∨ q
Question 12 [5 Marks]
Construct formal proof of validity:
1. (E ∨ F) · (G ∨ H)
2. (E ⊃ G) · (F ⊃ H)
3. ~G / ∴ H
4. E ∨ F (1, Simp)
5. G ∨ H (4, 2, CD)
6. H (5, 3, DS)
UNIT-V
Question 13 [1 × 3 = 3 Marks]
(a) What is hypothesis?
A hypothesis is a tentative explanation or an educated guess made as a starting point for further investigation
.(b) Define science.
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Question 15 [5 Marks]
Option BDiscuss the role of hypothesis in scientific enquiry.
The hypothesis serves as the guiding light of scientific enquiry
.Exam Preparation Hub
Exam Tips
Important Formulas
- Modus Ponens (MP): p ⊃ q, p / ∴ q
- De Morgan's (De M.): ~(p · q) ≡ (~p ∨ ~q)
Answer Presentation Strategy
In Unit II truth tables, clearly label your final column as "Result" and state if it is a Tautology, Contradiction, or Contingent
.