Deductive Logic

Deductive logic is a way of reasoning where we start with general statements that we assume are true, and from them we derive specific conclusions that must be true. Unlike induction, deductive reasoning gives certainty — if the starting statements are true, the conclusion cannot be false.

Definition

In deductive logic, we take one or more general statements (called premises) and use rules of logic to reach a conclusion. The conclusion follows with necessity — it is guaranteed, provided the premises are correct.

Examples

• Premise 1: All humans are mortal.
  Premise 2: Socrates is a human.
  Conclusion: Socrates is mortal.


• Premise 1: If it rains, the ground gets wet.
  Premise 2: It is raining.
  Conclusion: The ground is wet.


• Premise 1: All even numbers are divisible by 2.
  Premise 2: 8 is an even number.
  Conclusion: 8 is divisible by 2.

Key Point

Deductive reasoning starts from statements that we accept as true and uses logical steps to reach a conclusion that must be true. This is the type of reasoning used in mathematics and formal proofs.

For Mathematics:

Deductive Logic is more popular and used in higher mathematics where we have strongly accepted premises such as axioms of geometry and we build further theorems from them.

Some Practice Exercises: