Final answer:
The relation wherein individuals a and b have the same parents is an equivalence relation because it satisfies all properties required: reflexivity, symmetry, and transitivity. Therefore, the given statement is false.
Step-by-step explanation:
The relation a and b have the same parents is indeed an equivalence relation. An equivalence relation on a set must satisfy three properties: reflexivity, symmetry, and transitivity.
- Reflexivity: For any person a, clearly a has the same parents as a, so (a, a) is in the relation.
- Symmetry: If (a, b) is in the relation, meaning a and b have the same parents, then (b, a) is also in the relation since b and a have the same parents.
- Transitivity: If (a, b) and (b, c) are in the relation, then a and b have the same parents, and b and c have the same parents, so a and c must have the same parents, making (a, c) also in the relation.
Since the relation satisfies all the required properties for an equivalence relation, the statement is false.