GATE 2008
March 14, 2025GATE 1987
March 15, 2025GATE 1987
| Question 4 |
The union of two equivalence relations is also an equivalence relation.
| True | |
| False |
Question 4 Explanation:
Equivalence relation should satisfy Reflexive, Symmetric and Transitive property.
Reflexive ∪ Reflexive = Reflexive
Symmetric ∪ Symmetric = Symmetric
Transitive ∪ Transitive ≠ Transitive
Since Transitivity does not satisfy union, so union of two equivalence relation is not an equivalence relation.
Reflexive ∪ Reflexive = Reflexive
Symmetric ∪ Symmetric = Symmetric
Transitive ∪ Transitive ≠ Transitive
Since Transitivity does not satisfy union, so union of two equivalence relation is not an equivalence relation.
Correct Answer: B
Question 4 Explanation:
Equivalence relation should satisfy Reflexive, Symmetric and Transitive property.
Reflexive ∪ Reflexive = Reflexive
Symmetric ∪ Symmetric = Symmetric
Transitive ∪ Transitive ≠ Transitive
Since Transitivity does not satisfy union, so union of two equivalence relation is not an equivalence relation.
Reflexive ∪ Reflexive = Reflexive
Symmetric ∪ Symmetric = Symmetric
Transitive ∪ Transitive ≠ Transitive
Since Transitivity does not satisfy union, so union of two equivalence relation is not an equivalence relation.