Explanation:
Plain carbon steel is an alloy of iron and carbon, where carbon is the main alloying element. The carbon content in plain carbon steel can vary from 0.05% to 2.0%. The properties of plain carbon steel are influenced by the carbon content.

Tensile Strength:
Tensile strength refers to the ability of a material to resist deformation under tensile forces. It is a measure of how much stress a material can withstand before it fails. The tensile strength of plain carbon steel increases with an increase in carbon content. This is because the carbon atoms in the steel matrix occupy the interstitial spaces between the iron atoms, leading to increased strength and hardness.

Hardness:
Hardness is a measure of a material's resistance to indentation or scratching. It is directly related to the strength of the material. An increase in carbon content in plain carbon steel leads to an increase in hardness. This is because the carbon atoms form iron carbide (Fe3C) precipitates, which increase the hardness of the steel.

Malleability:
Malleability refers to the ability of a material to be deformed under compression without fracturing. An increase in carbon content in plain carbon steel decreases its malleability. This is because the presence of carbon atoms increases the likelihood of the formation of brittle iron carbide (Fe3C) precipitates, which reduce the material's ability to deform under compression.

Ductility:
Ductility refers to the ability of a material to be deformed under tensile forces without fracturing. An increase in carbon content in plain carbon steel decreases its ductility. This is because the presence of carbon atoms increases the likelihood of the formation of brittle iron carbide (Fe3C) precipitates, which reduce the material's ability to deform under tension.

Therefore, an increase in carbon content in plain carbon steel raises its tensile strength and hardness, but decreases its malleability and ductility.