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1. Set Theory
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Students : computer science DPE
Prepared by :
Roman Sabah
Brwa Star
Muhammed Anwar
Mustafa Yusuf
Shahin Abdulla
Supervisor : M.Bazhdar
Koya University - Koya
College Faculty of Science and
Health Department of Computer
Science Department

2. OUTLINE
1. What is set theory ?
2. What is empty set (null set) ?
3. What is finite set and infinite set ?
4. What is proper subset ?
5. What is improper subset ?
6. What is subset ?
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What is set theory ?
Set theory is a branch of mathematical logic
that studies sets, which are collections of
objects. These objects can be anything
numbers, letters, colors, or even other sets.
Set theory was developed to provide a
foundation for the rest of mathematics. It
was formalized by the German
mathematician Georg Cantor in the late
19th century.

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What is empty set (null set)?
In calculus, the empty set, denoted by ∅ or {}, is a set that contains no elements. It is often encountered in situations
where a solution or a set of values is expected, but none fulfill the given conditions.
For example, consider the solution set to the equation (x^2 = -1) over the real numbers. Since there is no real
number whose square is -1, the solution set is the empty set: ({ } ) or ∅.
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5. What is finite set and infinite set ?
A finite set is a set that contains a definite number of elements. In other words, a set is considered finite if it has a specific,
countable number of elements. For example, the set {1, 2, 3} is a finite set because it contains three elements, and you can
count them.
On the other hand, an infinite set is a set that contains an infinite number of elements. These sets cannot be counted or
exhausted, as they go on indefinitely. An example of an infinite set is the set of all natural numbers {1, 2, 3, 4, ...}.
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6. What is proper subset ?
A proper subset of a set A
is a subset of A
that is not equal to A
. In other words, if B
is a proper subset of A
, then all elements of B
are in A
but A
contains at least one element that is not in B.
For example, if A={1,3,5}
then B={1,5}
is a proper subset of A
. The set C={1,3,5}
is a subset of A
, but it is not a proper subset of A
since C=A
. The set D={1,4}
is not even a subset of A
, since 4 is not an element of A.
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7. What is improper subset ?
What is Improper Subset?
A subset which contains all the elements of the
original set is called an improper subset. It is
denoted by ⊆.
For example: Set P ={2,4,6} Then, the subsets of
P are;
{}, {2}, {4}, {6}, {2,4}, {4,6}, {2,6} and {2,4,6}
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8. What is subset ?
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subset : A subset is a segment of a larger set (another set or the same set). To denote a set A as a subset of set
B, use the set notation: A ⊆ B.
EX : If A is the set of natural numbers and B is the set of all whole numbers, then A is a subset of B (since the
set of whole numbers contains all natural numbers).

9. Reference :
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• https://testbook.com/learn/maths-types-of-sets/> [Accessed 25 April
2022].
• https://byjus.com/maths/subsets/#:~:text=What%20is%20Improper%2
0Subset%3F,2%2C4%2C6%7D.
• Introduction to the Theory of Sets" by Joseph Breuer and Azriel Levy :
Book.

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