Concept:
Fiber properties such as hydrophobicity (water-repelling) and hydrophilicity (water-absorbing) determine the functional end-use of fabrics.
Step 1: Evaluate Assertion (A).
Nylon and Polyester are synthetic, thermoplastic fibers. They are naturally hydrophobic, meaning they absorb very little water (low moisture regain). Because they do not soak up water into the fiber core, they dry very quickly when hung up, which is known as the "drip dry" property. Thus, Assertion (A) is correct.
Step 2: Evaluate Reason (R).
Cotton is a highly hydrophilic fiber. It absorbs moisture (sweat) but holds onto it, becoming heavy, damp, and slow to dry. For high-performance sportswear, a "dry-feel" is actually achieved using synthetic wicking fabrics (like treated polyester) that move sweat away from the skin to the fabric surface to evaporate. Therefore, Reason (R) is factually incorrect as cotton is generally avoided for professional "dry-feel" sportswear.