## Equal set writing method

**Two sets A and B** are equal that is **A=B** if and only if we have the same elements that is **if and only** **if** every element of **each set** is an element of the **other set** .thus the equal set writing sets **{3,4,5}** and **{4,3,5}** are equal. From the **definition of equality of sets**, it follows that the mere change in the order of the elements of a set does not alter the set. In other words, while describing a set in the **tabular** form, its element may be writing in the order.

**EXAMPLE:**

** A ={3,4,5} and set B= {4,3,5}**

we arrange the number in set B = {3,4,5}

**then the set {4,3,5} and {3,4,5}**

** thus A=B**

**NOTE:**

(a) A=B if and only if they have the same element means if A=B they have the same elements and if A and B have the same element then A =B

(b) the symbol **if and only if** denoted by ” **iff** ” mathematically writing

**EQUIVALENTS SET:**

If the element of **two sets A and B can be paired** in such a way that each element of A is paired with one and only one element of is paired with **one and only one** element of B and so on…. then such a pairing is called** one to one correspondence between A and B.**

**EXAMPLE:**

A= {Tapir, Gama, Basher} and set B= {Asia, Fatima, Sami} then the six (1,-1) different correspondence can be established between A and B **(i) (Tapir, Gama, Basher)**

** (Asia, Fatima, Sami)**

**(ii) (Tapir, Gama, Basher)**

**(Asia, Sami, Fatima)**

we can write four remaining correspondence

Two set are said to be equivalent if a (1, -1) correspondence can be established between them.

**EXAMPLE:**

consider the set N= {1,2,3………….} and E = {2,4,6,……………..}

We can establish (1, -1) correspondence between them.

(1,2,3…………..)

(2,4,6……………)

**thus, the set N and E are equivalent. But notice that they are not equal.**

Remember that two equal sets are necessary equivalent. But the converse

may not be true That is two equivalent sets are not necessarily equal

**Equivalent sets symbol:**

sometimes the symbol ** ∼ ** is used equivalent sets to, Thus **N ∼ E**

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