What is Proposition?
The meaning of proposition in literature is an idea, a plan an offer, or a suggestion that can be proved True or False. The same goes for mathematical propositions. They are declarative sentences that can be True or False. Propositions are the fundamental building blocks of logic.
Examples:
1. The magnetic lines emerge from the North and merge into South pole.
2. 2 + 1 = 3
3. ‘p’ is a vowel.
All of the above three sentences are proper propositions, where the first two are True and the third one is False.
Problems on Tautology
In discrete mathematics, a tautology is a compound statement that is always true, regardless of the truth values of its individual components. It is a fundamental concept in propositional logic, used to verify logical expressions and implications. Tautologies play a crucial role in constructing proofs and understanding logical consistency.
Table of Content
- What is Proposition?
- Tautology
- Truth Table
- Problems on Tautology
- 1) P
- 2) P⇒P
- 3) (P ⇒ P) ⇒ P
- 4) (p → q) → [(p → q) → q]
- 5) ((P⇒Q)∧P)⇒Q
- Practice Problems on Tautology