Which of the following polymers involves cross-linkages.

To determine which of the following polymers involves cross-linkages, we need to analyze each option. Cross-linkages refer to the formation of chemical bonds between polymer chains, resulting in a three-dimensional network structure.

1. Polyethylene (PE): Polyethylene is a linear polymer composed of repeating ethylene monomers. It does not involve cross-linkages and exists as a long, flexible chain.

2. Polypropylene (PP): Similar to polyethylene, polypropylene is a linear polymer made up of propylene monomers. It also does not involve cross-linkages and has a linear structure.

3. Polyvinyl chloride (PVC): PVC is a polymer that can involve cross-linkages. By adding a cross-linking agent, such as a peroxide, to the PVC polymer, cross-linking can occur, resulting in a more rigid and heat-resistant material.

4. Polyethylene terephthalate (PET): PET is a linear polymer commonly used in plastic bottles. It does not involve cross-linkages and has a linear structure.

Based on the analysis, the polymer that involves cross-linkages is polyvinyl chloride (PVC).