What We Have Discussed

1. A set is a well-defined collection of distinct objects. "Well-defined" means:

(i) There is a universe of objects which are allowed into consideration.

(ii) Any object in the universe is either an element of the set or not an elementan element.

2. An object belonging to a set is known as an element of the set. We use the symbol ‘∈’ to denote membership of an element and read it as belongs tonot belongs to.

3. Sets can be written in the roster form where all elements of the set are written, separated by commas, within brackets.

4. Sets can also be written in the form.

5. A set which does not contain any element is called an set, or a set, or a set.

6. A set is called a finite set if its / is a whole number.

7. We can say that a set is infinite if it is not finitefinite.

8. The number of elements in a finite set is called the / of the set.

9. The universal set is denoted by U or ξ.

10. A subset of B if ‘a’ is an element of A implies that ‘a’ is also an element of B. This is written as A ⊆ B if a ∈ A ⇒ a ∈ B, where A and B are two sets.

11. Two sets, A and B, are said to be equalunequal if every element in A belongs to B and every element in B belongs to A.

12. A union B is written as A ∪ B = {x : x ∈ A or x ∈ B}.

13. A intersection B is written as A ∩ B = {x : x ∈ A and x ∈ B}.

14. The difference of two sets A and B is defined as .

15. A - B = {x : x ∈ A} and x ∉ B.

16. diagrams are a convenient way of showing operations between sets.