Intersection of Sets

When two sets are intersected, a new set is formed containing the elements found in both the first set and the second set. In other words, the elements that are shared by both sets are found in the intersection.

The intersection of sets is denoted by $\cap$.

Examples

By using the sets A, B, C and D from the previous page:

$A\cap B=\left\{1,2,3,4\right\}\cap \left\{4,5,6,7\right\}=\left\{4\right\}$

$B\cap C=\left\{4,5,6,7\right\}\cap \left\{4,5\right\}=\left\{4,5\right\}=C$

$C\cap D=\left\{4,5\right\}\cap \left\{9\right\}=$$\varnothing$

$\left(A\cup B\right)\cap C=\left(\left\{1,2,3,4\right\}\cup \left\{4,5,6,7\right\}\right)\cap C$

$=\left\{1,2,3,4,5,6,7\right\}\cap \left\{4,5\right\}$

$=\left\{4,5\right\}$

$=C$

 

Note: In the second example, the result of the intersection happens to be one of the defined sets. In the third example, we got the empty set $\varnothing$ and so the sets are said to be disjoint.

 

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