Amitesh Kumar
A proposition or a statement or a logical sentence is a declarative sentence that can be either true or false.
Example of Propositions
- Jawaharlal Nehru was the first prime minister of India.
- Today is Monday.
Example of Non-Propositions
- What is your name?
- Please come in.
Propositional Variable
The lowercase letters starting with P are used to represent the proposition.
Example
p: Mahatma Gandhi is the father of India.
q: 2+2 = 4
Compound Propositions
A statement or propositional variable can be combined with logical connectives (logical operators) to form a single statement will be a compound statement or compound proposition.
There are five logical operators:
| Symbol | Connective | Name |
| ~ | Not | Negation |
| ^ | And | Conjunction |
| v | Or | Disjunction |
| ⟶ | Implies or If…then | Implication or Conditional |
| ⟷ | if and only if | Equivalence or Biconditional |
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