Course Content
Sets
A set is a collection of elements or numbers or objects, represented within the curly brackets { }. For example: {1,2,3,4} is a set of numbers. There are three forms in which we can represent the sets. They are: Statement form: A set of even number less than 20 Roster form: A = {2,4,6,8,10,12,14,16,18} Set builder form: A = {x: x=2n, n ∈ N and 1 ≤ n ≤ 20}
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Venn Diagrams
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When we define a set, if we take pieces from that set, we can form what is called a subset.
Example: The set { 1, 2, 3, 4, 5}

A subset of this is { 1, 2, 3}. Another subset is {4, 5 }. Another is { 1 }

But {1, 6 } is not a subset since it has an element {6} that is not in the parent set

In general: A is a subset of B if and only if every element of A is in B

Universal Set

The set under consideration is likely 10 be the subsets of a fixed or a global set. This fixed or global set is called the Universal Set. A universal set is the set of all objects of interest in a particular discussion. This set can be very big or small depending on the context

For example, if we are discussing medical students at Nnamdi Azikwe University, the whole students of the Nnamdi Azikwe University can be our universal set. If our reference is to persons, every person in the Nnamdi Azikwe University can be the universal set. Therefore, the universal set varies as our group of references varies. The universal set is usually denoted by U

Equal Set

Two sets are equal If they have precisely the same members. Now, at first glance they may not seem equal, we may have to examine them closely

Example: Are A and B equal? Where
A is the set whose members are the first four positive whole numbers

B= {4, 2, 1, 3 }

Let’s check. They both contain 1,2,3,4 So they are equal.

The equals sign (=) is used to show equality.

Therefore, A= B

Empty or Null Set

There are no elements in this set. It is represented by { } or Ø

Singleton Set

If a set contains only one clement. It is said to be a singleton element

Hence, the sets {7}. {8} and {1} are singleton sets.

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