diff --git a/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/NonEmptySet.java b/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/NonEmptySet.java
index b574733f..5b5dcf2a 100644
--- a/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/NonEmptySet.java
+++ b/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/NonEmptySet.java
@@ -28,6 +28,6 @@ default boolean isEmpty() {
 
 	// TODO: the cardinality of the union is actually not known
 	// at this point:
-	return new Union<E, C>(this, (NonEmptySet<E, ?, ?>) cpl);
+	return new Union<E, C>((NonEmptySet<E, ?, ?>) cpl, (NonEmptySet<E, ?, ?>) that);
     }
 }
diff --git a/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/SingletonSet.java b/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/SingletonSet.java
index 5ca379a6..56cd7682 100644
--- a/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/SingletonSet.java
+++ b/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/SingletonSet.java
@@ -16,7 +16,12 @@ public interface SingletonSet<E extends Element<E>, S extends SingletonSet<E, S>
 FiniteSet.B64<E, Small.One, S>
 {
     E elem();
-    
+
+    @Override
+    default boolean contains(E that) {
+	return elem().eq(that);
+    }
+
     @Override
     default Set<E, ? extends Small.One, ?> where(Predicate<E> Φ) {
 	return Φ.test(elem()) ? this : EmptySet.empty();
diff --git a/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/Union.java b/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/Union.java
index 9226d69b..012a64a7 100644
--- a/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/Union.java
+++ b/dedekind-ontology/src/main/java/com/github/vincentk/dedekind/sets/Union.java
@@ -13,6 +13,12 @@ record Union<
 implements
 NonEmptySet<E, C, Union<E, C>>
 {
+    @Override
+    public boolean
+    contains(E elem) {
+	return fst().contains(elem) || snd().contains(elem);
+    }
+    
     @Override
     public
     Set<E, ?, ?>
diff --git a/dedekind-ontology/src/test/java/com/github/vincentk/dedekind/sets/UnionTest.java b/dedekind-ontology/src/test/java/com/github/vincentk/dedekind/sets/UnionTest.java
new file mode 100644
index 00000000..1c5bfa95
--- /dev/null
+++ b/dedekind-ontology/src/test/java/com/github/vincentk/dedekind/sets/UnionTest.java
@@ -0,0 +1,56 @@
+package com.github.vincentk.dedekind.sets;
+
+import static org.assertj.core.api.Assertions.assertThat;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+import com.github.vincentk.dedekind.algebra.numbers.N;
+
+public class UnionTest {
+
+    private static final SingletonSet<N.N63.Ne, ?> S1 = new SingletonSet.Ordered.Default<>(N.ONE);
+    private static final SingletonSet<N.N63.Ne, ?> S2 = new SingletonSet.Ordered.Default<>(N.TWO);
+    private static final EmptySet<N.N63.Ne> EMPTY = EmptySet.empty();
+
+    @Test
+    public void testConstruction() {
+	assertThat(EMPTY.union(EMPTY)).isEqualTo(EMPTY);
+	assertThat(S1.union(EMPTY)).isEqualTo(S1);
+	assertThat(EMPTY.union(S1)).isEqualTo(S1);
+	assertThat(S1.union(S1)).isEqualTo(S1);
+
+	final var u2 = S1.union(S2);
+	assertThat(u2).isInstanceOf(Union.class);
+	assertThat(u2.contains(N.ONE)).isTrue();
+	assertThat(u2.contains(N.TWO)).isTrue();
+    }
+
+    @Test
+    public void testEmptySet() {
+
+	final var SUBJECT = S1.union(S1);
+
+	assertTrue(SUBJECT.eq(SUBJECT));
+
+	assertThat(SUBJECT.intersection(SUBJECT)).isEqualTo(SUBJECT);
+
+	assertThat(SUBJECT.union(SUBJECT)).isEqualTo(SUBJECT);
+
+	assertThat(SUBJECT.sub(SUBJECT))
+	.as(() -> "The empty set is a subset of itself.")
+	.isTrue();
+
+	assertThat(SUBJECT.sup(SUBJECT))
+	.as(() -> "The empty set is a super-set of itself.")
+	.isTrue();
+
+	assertThat(SUBJECT.where(x -> true))
+	.as(() -> "A conditioned empty set is still empty.")
+	.isEqualTo(SUBJECT);
+
+	assertThat(SUBJECT.complement(SUBJECT))
+	.as(() -> "The difference between the empty set and itself empty.")
+	.isEqualTo(EmptySet.empty());
+    }
+}