Let cardinality of set A be 16 and cardinality of set of all equivalence…
2015
Let cardinality of set A be 16 and cardinality of set of all equivalence classes under some equivalence relation on A be 4. Then the number of elements in each equivalence class is:
- A.
2
- B.
4
- C.
6
- D.
8
- E.
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Correct answer: B
An equivalence relation partitions a set into disjoint equivalence classes, and all elements of the set belong to exactly one class.
Given:
Total elements in set A=16
Number of equivalence classes = 4
Assuming each class has equal size (since otherwise it’s not uniquely determined):
Size of each class=16/4=4
Each equivalence class has 4 elements.