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



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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 QQ P⇒QP \Rightarrow Q
T T T
T F F
F T T
F F T

4. Applications of Propositions

  • Boolean Algebra (Digital Circuits)

  • Programming (Conditional Statements, Loops)

  • Database Queries (SQL Logic)

  • Artificial Intelligence (Logical Reasoning)

  • Mathematical Proofs (Induction, Deduction)

Would you like examples or GATE-level problems on this?

Day 04 Part 01- Discrete Mathematics for gate in Hindi-Proposition and it’s application

Discrete Mathematics and Its Applications, Eighth Edition

Discrete Mathematics for Computer Science

Discrete Mathematical Structures



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