Let E1, E2 Equivalence relations on A, Prove or disprove :

Question

Let E1, E2 Equivalence relations on A, Prove or disprove :

1) E1 ∩ E2 an equivalence relation on A

2) E1 ∪ E2 an equivalence relation on A

Answer 1

Statement 1 is true. You should prove that the new relation is reflexive, symmetric and transitive.

Statement 2 is false. You should try to make a counterexample in which transitivity fails. Try $A=\{1,2,3\}$.