DISCRETE STRUCTURES (MCA) – LESSON 1
🔹 TOPIC: TAUTOLOGY, CONTRADICTION & CONTINGENCY
This topic is 100% guaranteed in your exam.
1️⃣ What is a Proposition?
A proposition is a statement that is either TRUE or FALSE, but not both.
Examples:
“2 + 2 = 4” ✅ (True)
“5 is even” ❌ (False)
❌ Not propositions:
“Close the door”
“x + 2 = 5” (value of x not fixed)
2️⃣ Logical Operators (Quick Revision)
Symbol
Meaning
Name
¬P
Not P
P ∧ Q
P and Q
P ∨ Q
P or Q
P → Q
If P then Q
P ↔ Q
P if and only if Q
3️⃣ TAUTOLOGY (🔥 VERY IMPORTANT)
📌 Definition:
A tautology is a compound proposition that is TRUE for all possible truth values of its variables.
Example:
P
¬P
P ∨ ¬P
T
F
T
F
T
T
✔ Always TRUE → Tautology
Exam Line ✍️:
A tautology is a proposition which is true for all truth values of its variables.
4️⃣ CONTRADICTION
📌 Definition:
A contradiction is a proposition that is FALSE for all truth values.
Example:
P
¬P
P ∧ ¬P
T
F
F
F
T
F
❌ Always FALSE → Contradiction
Exam Line ✍️:
A contradiction is a proposition which is false for all truth values.
5️⃣ CONTINGENCY
📌 Definition:
A contingency is a proposition that is sometimes true and sometimes false.
Example:
P
Q
P → Q
T
T
T
T
F
F
F
T
T
F
F
T
✔ Mixed values → Contingency
6️⃣ ONE-MARK DIFFERENCE (VERY IMPORTANT)
Term
Always True
Always False
Mixed
Tautology
✅
❌
❌
Contradiction
❌
✅
❌
Contingency
❌
❌
✅
🧠 QUICK CHECK (Answer in your mind)
Is � a tautology?
Is � a contradiction?
(We’ll solve these next)
📌 EXAM WRITING TEMPLATE (MEMORIZE)
Q. Explain tautology with example.
Answer:
A tautology is a compound proposition which is true for all possible truth values of its variables.
Example: �.
The truth table shows the result is always true, hence it is a tautology.
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