(i) Enantiomers: Enantiomers are pairs of molecules that are non-superimposable mirror images of each other. They have identical physical properties but differ in their interaction with plane-polarized light and in the way they interact with other chiral substances. For example, the right- and left-handed forms of a chiral molecule are enantiomers.
(ii) Racemic mixture: A racemic mixture is a mixture containing equal amounts of two enantiomers of a chiral compound. In a racemic mixture, the optical activities of the enantiomers cancel each other out, resulting in no net optical rotation.
The incorrect statements regarding geometrical isomerism are:
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene.
(D) 2-methylbut-2-ene shows two geometrical isomers.
(E) Trans-isomer has lower melting point than cis isomer.
Given below are two statements:
Statement (I):
are isomeric compounds.
Statement (II): are functional group isomers.
In the light of the above statements, choose the correct answer from the options given below:
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\} $.