Introduction to set operations III — lesson. Mathematics State Board, Class 9.

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Disjoint set:

Two sets

$A$ and

$B$ are said to be disjoint if they do not have any element in common for two sets

$A$ and

$B$ .

Symbolically we write

$A\cap B=\varnothing$ (where

$\varnothing$ is empty set).

$\begin{array}{l} A = {2, 4, 6, 8}, B = {10, 12}. \\ A \cap B = {2, 4, 6, 8} \cap {10, 12} \end{array}$

Where no common elements are in the set

$A$ and

$B$ .

$A$ and

$B$ are disjoint.

So,

$A\cap B=\varnothing$

Important!

$A$ and

$B$ do not have any element in common and are disjoint sets.

Overlapping sets:

Two sets

$A$ and

$B$ are said to be overlapping if they contain at least one element in common from two sets

$A$ and

$B$ .

Symbolically we write

$A\cap B\neq \varnothing$ (where

$\varnothing$ is empty set\).

$\begin{array}{l} A = {2, 4, 6, 8}, B = {6, 8, 10, 12}. \\ A \cap B = {2, 4, 6, 8} \cap B = {6, 8, 10, 12} \end{array}$

Where, at least one common element is in both the set

$A$ and

$B$ .

Because

$A$ and

$B$ are overlapping.

So,

$A\cap B=\{6,\ 8\}\neq\varnothing$

Therefore,

$A\cap B\neq\varnothing$

In the Venn diagram below, the area in the blue colour represents

$A \cap B \neq \emptyset$ .

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3. Introduction to set operations III

Theory: