Azeotrope: An azeotrope is a mixture of two or more liquids that behaves as a single substance when boiled. This means that the composition of the vapor produced during boiling is the same as the composition of the liquid, and thus it cannot be separated by simple distillation. Azeotropes occur because of the specific interactions between the components in the mixture.
Azeotrope formed by negative deviation from Raoult's law: In mixtures that show a negative deviation from Raoult’s law, the intermolecular forces between the components are stronger than those in the individual pure components. This leads to a lower vapor pressure than expected, and the mixture boils at a lower temperature than either of the pure liquids. This behavior often leads to the formation of an azeotrope. An example of an azeotrope formed by a negative deviation is the water and hydrochloric acid (HCl) mixture. The HCl solution in water forms an azeotrope at around 20.2% HCl by weight, which boils at 108.6°C. At this composition, it cannot be separated further by distillation, as the vapor has the same composition as the liquid.
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.