Mathematics Quick Revision of sets from Key Diagrams
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representation of a set in roster and set- builder form

The Empty set

Finite and Infinite Sets & Cardinality of a Finite Set

Equal and Equivalent sets

Subset, Proper Subset and Superset

Intervals as subsets of R

Power set

Universal set

Venn Diagram

• A `\color{blue} ul(\mathtt ( \ \ VENN \ \ Diagram))` is a diagram that uses closed curves to illustrate the relationships among sets.

• These diagrams consist of rectangles and closed curves usually circles or ellipses. The universal set is represented usually by a rectangle and its subsets by circles or ellipses.

E.g. 1 : In Fiig.`1 \ \ ` `U = {1,2,3, ..., 10}` is the universal set of which `A = {2,4,6,8,10}` is a subset.

Union of sets

`"Definition"` The union of two sets `A` and `B` is the set `C` which consists of all those elements which are either in `A` or in `B` (including those which are in both).

we write `A ∪ B` and usually read as `"‘A union B’."`

Intersection of sets

• The intersection of two sets A and B is the set of all those elements which `"belong to both A and B."`

• The symbol `‘∩’` is used to denote the intersection.

`star \ \ "Disjoint sets"`

• If `A` and `B` are two sets such that `A ∩ B = Phi ,` then `A` and `B` are called disjoint sets.

Difference of sets (A-B) or (A/B) :

• The difference of the sets `A` and `B` in this order is the set of elements which ` "belong to A but not to B." `

• Symbolically, we write `A – B` and read as `"“ A minus B”"`

Complement of a Set

• Let `U` be the universal set and `A` a subset of `U.` Then the complement of `A` is the set of all elements of `U` which are not the elements of `A.`

• Symbolically, we write `A′` to denote the complement of `A` with respect to `U.`