Theory:

Elements are the fundamental substances that cannot be separated into simpler substances by any chemical methods. All the elements in the periodic table is an example for elements such as Oxygen, Iron, etc.
Let's now see how the symbols for elements are given:
 
1. For the most common elements, like non-metals, use the first letter of the English name. For example,
 
Element
Symbol
Boron
\(B\)
Carbon
\(C\)
Fluorine
\(F\)
Oxygen
\(O\)
Iodine
\(I\)
 
2. If the name of an element has the same letter as another, use the first and second letter of their English name—the first letter in upper case and the second letter in lower case. For example,
 
Element
Symbol
Boron
\(B\)
Barium
\(Ba\)
Beryllium
\(Be\)
Bismuth
\(Bi\)
Bromine
\(Br\)
 
3. If the first letter or first two letters of the element is the same as another, use the first and second or third letter of the English name.
 
Element
Symbol
Argon
\(Ar\)
Arsenic
\(As\)
Chlorine
\(Cl\)
Chromium
\(Cr\)
Magnesium
\(Mg\)
Manganese
\(Mn\)
  
4. Some of the elements are named using the old or Latin name of the element. There are eleven elements. Few of them are listed here.
 
Element
Latin name
Symbol
Sodium
Natrium
\(Na\)
Potassium
Kalium
\(K\)
Iron
Ferrum
\(Fe\)
Copper
Cupurum
\(Cu\)
Gold
Aurum
\(Au\)
Tin
Stannum
\(Sn\)
 
5. Some of the elements are named after the name of country, scientist, colour, mythological character or planet.
 
Name
Symbol
Name derived from
Americium
\(Am\)
America (country)
Europium
\(Eu\)
Europe (country)
Nobelium
\(No\)
Alfred Nobel (scientist)
Iodine
\(I\)
Violet (colour, Greek)
Mercury
\(Hg\)
Gold Mercury (mythological character)
Uranium
\(U\)
Uranus (planet)
 
These are few rules that were used to write a chemical symbol of an element in the periodic table.