What is the difference between set theory and logic?

What is the difference between set theory and logic?

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. Logic, on the other hand, is the study of reasoning and argumentation. While set theory focuses on the properties and relations of sets, logic deals with the principles of valid inference and demonstration.

Can you give me an example of how they are used differently?

Sure! In set theory, you might define a set of all even numbers, while in logic, you might analyze the validity of the argument: 'If all humans are mortal, and Socrates is a human, then Socrates is mortal.' The former is about collections, and the latter is about reasoning.

Are there any overlaps between the two fields?

Yes, there are overlaps! For instance, set theory can be used within logic to define the domain of discourse, and logical operations can be applied to sets, such as union and intersection.

Which one is more foundational in mathematics?

Set theory is often considered more foundational because it provides a basis for most mathematical concepts, while logic underpins the reasoning processes used in mathematics.