How to decompose water into oxygen and hydrogen

How to decompose water into oxygen and hydrogen

Electrolysis
The process of decomposing a compound by electricity is called electrolysis.
Water (H2O) is electrolyzed to produce electrolyzed water. When current passes through water (H20), hydrogen is formed at the cathode and oxygen is formed at the anode. The positively charged ions move toward the cathode and dissolve in the minerals calcium, magnesium, potassium, sodium... The positively charged ions form at the cathode, the alkaline water we drink, and the negatively charged ions form at the anode.
The chlorine added to the tap water is also discharged into the anodic acid water, which is virtually undetectable due to the pre-filtration system and the built-in antimicrobial silver-loaded activated carbon.
The principle of electrolysis seems simple, but it is not easy to generate electrolytic water quickly and safely. After continuous improvement, manufacturers began to use safe and stable titanium as electrodes

Water electrolysis can produce hydrogen and oxygen, so the water contains hydrogen and oxygen Why is this sentence wrong?

Hydrogen and oxygen require molecules to exist to be present.
There are only hydrogen atoms and oxygen atoms in water
Hydrogen atoms do not represent hydrogen molecules, and oxygen atoms do not represent oxygen molecules.

Hydrogen and oxygen require molecules to be present.
There are only hydrogen atoms and oxygen atoms in water
Hydrogen atoms do not represent hydrogen molecules, and oxygen atoms do not represent oxygen molecules.