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Sets

A set is a collection of distinct elements. The union contains everything that is in at least one of the sets, and the intersection what is in both. The size of a union is found by inclusion and exclusion, so nobody is counted twice.

A \cup B

union: in A or B

A \cap B

intersection: in both A and B

|A \cup B| = |A| + |B| - |A \cap B|

inclusion and exclusion

Symbols

$\|A\|$	number of elements in A
$\in$	is an element of
$\emptyset$	empty set

Example

30 students take maths, 20 physics and 12 both:

$|M \cup F| = 30 + 20 - 12 = 38$ .

Subtract the intersection, or you count those in both twice.

Practise logic and sets for free →

← De Morgan's laws · The multiplication principle →

Part of Discrete Mathematics: Logic and sets.