The document defines sets and subsets. A set is a collection of well-defined objects. An empty set contains no elements and is denoted by curly brackets. A proper subset A of set B contains all elements of A but at least one element of B is not in A. An improper subset occurs when sets A and B are equal with no extra elements in either set.

1. SETS AND SUBSET
CONCEPT AND DEFINITION

2. SETS
• A SET IS A COLLECTION OF WELL DEFINED OBJECTS
• EXAMPLE:
• THE COLLECTION OF ALL BEAUTIFUL FLOWERS IN OOTY
• THE COLLECTION OF ALL OLD MEN IN TAMIL NADU

3. EXAMPLE

4. EMPTY SET
• THE SET CONTAINING NO ELEMENTS IS CALLED EMPTY
SET
• IT IS DENOTED BY { }
• EXAMPLE:
• Consider set A = {x : 3 < x < 4, x is a whole number} and this set A is
the empty set, since there is no whole number between 3 and 4

5. ACTIVITY

6. ANSWER
• The square is 2, and the
circle is 1. So the answer
is also 1.

7. PROPER SUBSET
• A set A is a subset of another set B if all elements of the
set A are elements of the set B
• EXAMPLE:
• Set A is a proper subset of set B (A ⊂ B) if all of the elements of set A are
members of set B, but there is at least one element of set B that is not in A.

8. IMPROPER SUBSET
• A set A is called an Improper Subset of set B only when all
the members of set A and B are equal to each other and
there is no extra element in any of the sets.
• Improper Subsets can be also said to be Subsets. If a set
is an Improper Subset of another set, then both sets are
equal and have the same Cardinality.

9. DIFFERENCE BETWEEN PROPER AND IMPROPER
SUBSET: