Day 04 Part 01- Discrete Mathematics for gate in Hindi-Proposition and it’s application
Day 04 Part 01- Discrete Mathematics for gate in Hindi-Proposition and it’s application
Contents [hide]
- 1 Proposition and Its Applications (Discrete Mathematics for GATE – Day 04, Part 01)
- 2 Day 04 Part 01- Discrete Mathematics for gate in Hindi-Proposition and it’s application
- 3 Discrete Mathematics and Its Applications, Eighth Edition
- 4 Discrete Mathematics for Computer Science
- 5 Discrete Mathematical Structures
Proposition and Its Applications (Discrete Mathematics for GATE – Day 04, Part 01)
1. What is a Proposition?
A proposition is a declarative statement that is either true (T) or false (F) but not both simultaneously.
Examples:
“The sun rises in the east.” (True)
“2 + 2 = 5.” (False)
Non-examples (not propositions):
“What is your name?” (Not declarative)
“x + 5 = 10” (Truth value depends on x)
2. Logical Connectives
Propositions can be combined using logical operators:
Operator | Symbol | Example | Meaning |
---|---|---|---|
Negation | ¬P\neg P | “It is not raining” | Opposite truth value |
Conjunction | P∧QP \land Q | “It is cold and raining” | True if both are true |
Disjunction | P∨QP \lor Q | “It is cold or raining” | True if at least one is true |
Implication | P⇒QP \Rightarrow Q | “If it rains, then the road is wet” | False only if P is true and Q is false |
Biconditional | P⇔QP \Leftrightarrow Q | “You pass if and only if you study” | True when both have the same truth value |
3. Truth Table for Implication (→)
PP | P⇒QP \Rightarrow Q | |
---|---|---|
T | T | T |
T | F | F |
F | T | T |
F | F | T |
4. Applications of Propositions
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Boolean Algebra (Digital Circuits)
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Programming (Conditional Statements, Loops)
-
Database Queries (SQL Logic)
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Artificial Intelligence (Logical Reasoning)
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Mathematical Proofs (Induction, Deduction)
Would you like examples or GATE-level problems on this?