Engineering Mathematics, Volume I, Second Edition

15

Logic

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.

15.1 PROPOSITIONS

Definition 15.1 A declarative sentence that is either true or false, but not both is called a Proposition or a Statement.

EXAMPLE 15.1

Which of the following are propositions?

1. London is the capital of France
2. Open the door
3. Take two tablets of medicine
4. x + y > 0, x, y ∊ Z
5. The only positive integers that divide a prime number are 1 and the number itself.
6. The sun is hot

Solution.

1. The sentence is declarative and false. Hence, it is a proposition.
2. The sentence “Open the door” is not declarative. ...