Final answer:
In set theory, a relation is symmetric if all element pairs are mirrored, and anti-symmetric if no two different element pairs mirror each other (except for pairs of the same element, which can satisfy both). The symmetric and anti-symmetric properties mentioned relate to the electron density distribution in a hydrogen molecule model.
The correct answer is 1).
Step-by-step explanation:
To determine whether a relation is symmetric and/or anti-symmetric, we must first understand what these terms mean in the context of relations in set theory. A relation R on a set A is considered symmetric if for every pair (a, b) in the relation R, the pair (b, a) is also in R. It is anti-symmetric if for every pair (a, b) in the relation R where a ≠ b, the pair (b, a) is not in R.
In the context of the one-dimensional model of covalent bonding in a hydrogen molecule mentioned in the additional details, the symmetric wave function means that the electron density is the same on both sides of the molecule, reflecting a symmetric relation in the physical system.
Conversely, the anti-symmetric wave function describes a situation where the electron density distribution does not have this property, possibly reflecting an anti-symmetric relation.
It's important to note that a relation can be both symmetric and anti-symmetric if it includes only pairs of the same element, such as (a, a), because there is no contradiction between the definitions in this particular case.
The properties symmetric and anti-symmetric are not mutually exclusive, though in most practical situations, relations tend to be one or the other.
The correct answer is 1) Symmetric