# ALGEBRA OF SETS

**INTRODUCTION TO SET THEORY**

* Set theory* is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

**IDENTITY AND CARDINALITY OF SETS**

**Equality of sets or Identity of sets**

**:**A

**set**is said to be equal to set if both sets have the same elements or members of the sets, i.e. if each element of set also belongs to each element of set , and each element of set also belongs to each element of set .

**Mathematically**it can be written as A ⊂ B and B ⊂ A

In mathematics, the

**cardinality of a set**is a measure of the "number of elements of the set". For example, the set A = {2, 4, 16,24} contains 4 elements, and therefore A has a**cardinality**of 4.**SET OPERATIONS/SET THEORETICAL NOTATIONS**

The

**union**of two sets P and Q is a set containing all elements that are in P__or__in Q (possibly both). It is denoted by P∪Q.The

**intersection**of two sets P and Q, denoted by P∩Q, consists of all elements that are both in P and Q.The

**difference (subtraction)**is defined as follows. The set P−Q consists of elements that are in P but not in Q.**SET OF NUMBERS**

It is defined as any number that is, a solution to a polynomial equation with rational coefficients. All

**Rational****and****Irrational**numbers. They can also be**positive, negative****or****zero**.**Mathematically**, set of numbers can include:

**1)**Natural numbers,

**2)**Integers,

**3)**Rational numbers,

**4)**Irrational numbers,

**5)**Real numbers