Answer: The element a is not related to anything at all.
- A Symmetry and transitivity are incompatible properties
- B The element a is not related to anything at all
- C The relation must be the universal relation
- D The set must be infinite in such cases
Correct answer: B. The element a is not related to anything at all
Explanation: If a were related to some b, symmetry gives (b, a) and transitivity then forces (a, a) - so a must be isolated.
Concept context
Types of relations, equivalence classes, one-one and onto functions, composition, and invertible functions