What is the difference between using parentheses and brackets in interval notation when representing a set of real numbers?

Parentheses indicate that the endpoint is not included in the set, while brackets indicate that the endpoint is included in the set.

What is the symbol used to represent the empty set, and what does the empty set signify?

The symbol is φ (phi), and it represents a set with no elements.

I can define a set and use set notation to represent sets and subsets.

1
The intersection of two sets includes all the items that are common to both sets, while the union of two sets is the merging of the sets.
2
The intersection of the set of odd natural numbers and the set of even natural numbers is the empty set, also known as the null set, represented by the Greek letter phi.
3
Interval notation uses parentheses to imply non-inclusivity and brackets to imply inclusivity when representing solutions to inequalities.