Set Theory

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A set is a collection of objects, elements or members. The objects can be any collection you can think of. This collection can be described by listing the elements, or by giving a rule. The list or rule is given in a pair of curly brackets {}. For example: A={6,9,14} or B = { x :x2+5 |x }

The number of elements in the a set is given by n(A). For example: n(A)=3. The size of a set can be infinite.

∈ means is an element of;
∉ means is not an element of.
For example: 6A or 5B

The complement of a set A is the set of all the elements not in A and denoted by A

The empty set is denoted by Ø or {} and contains no elements.

The universal set is denoted by and contains all the elements of interest. This is how we show the universal set on a Venn diagram.

If a set A is completely overlaps by another set B then A is a sub set of B, AB. B is a proper subset of A if n(B)<n(A).


Set A is equal to B, A=B if and only if both contain exactly the same elements. So, {2,3,5} ={3,5,2}

Where A and B overlap then A intersects B, AB, or AandB. The elements listed by the intersection are on both sets.


Where we a looking for the members of two sets then this denoted by A union B, AB, or AorB. Here or is inclusive, that is, the union lists elements in one or the other set, or both.

n(AB) = n(A) +n(B) -n(AB)

De Morgan's Laws

(AB) = AB (AB) = AB

GCSE Set Theory 101

Set (mathematics) according to (Simple English Version)

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