From the Venn diagram given in the question, it can be concluded that Q is a natural fibre, R is a synthetic fibre and P is both natural as well as synthetic fibre, that is, semi-synthetic fibre.
P is a semi-synthetic fibre. Therefore, P can be a rayon.
Q is a natural fibre. Therefore Q can be cotton, silk or wool.
R is synthetic fibre. Therefore R can be polyester, nylon or acrylic.