Logic is the study of reasoning and is specifically concerned with whether a particular reasoning is valid. It is a science of the necessary laws of thought, without which no employment of the understanding and the reason takes place.
Definition 15.1 A declarative sentence that is either true or false, but not both is called a Proposition or a Statement.
Which of the following are propositions?
- London is the capital of France
- Open the door
- Take two tablets of medicine
- x + y > 0, x, y ∊ Z
- The only positive integers that divide a prime number are 1 and the number itself.
- The sun is hot
- The sentence is declarative and false. Hence, it is a proposition.
- The sentence “Open the door” is not declarative. ...