added more ∅ and U sets unit tests (#74)

test/unit/comparisons/disjoint.function.test.ts

@@ -58,10 +58,18 @@ function disjointTests<T>(testSets: TestSets<T>): void {
 		expect(disjoint(setA, empty)).toBe(true);
 	});
 
+	it('the empty set and any non-empty set are disjoint', () => {
+		expect(disjoint(empty, setA)).toBe(true);
+	});
+
 	it('any non-empty set and the universal set are not disjoint', () => {
 		expect(disjoint(setA, universal)).toBe(false);
 	});
 
+	it('the universal set and any non-empty set are not disjoint', () => {
+		expect(disjoint(universal, setA)).toBe(false);
+	});
+
 	it('the empty set is disjoint with itself', () => {
 		expect(disjoint(empty, empty)).toBe(true);
 	});

test/unit/comparisons/equivalence.function.test.ts

@@ -58,10 +58,18 @@ function equivalenceTests<T>(testSets: TestSets<T>): void {
 		expect(equivalence(setA, empty)).toBe(false);
 	});
 
+	it('the empty set and any non-empty set are not equivalent', () => {
+		expect(equivalence(empty, setA)).toBe(false);
+	});
+
 	it('any non-universal set and the universal set are not equivalent', () => {
 		expect(equivalence(setA, universal)).toBe(false);
 	});
 
+	it('the universal set and any non-universal set are not equivalent', () => {
+		expect(equivalence(universal, setA)).toBe(false);
+	});
+
 	it('the empty set is equivalent to itself', () => {
 		expect(equivalence(empty, empty)).toBe(true);
 	});

test/unit/comparisons/pairwise-disjoint.function.test.ts

@@ -58,10 +58,18 @@ function pairwiseDisjointTests<T>(testSets: TestSets<T>): void {
 		expect(pairwiseDisjoint(setA, empty)).toBe(true);
 	});
 
+	it('the empty set and any non-empty set are pairwise disjoint', () => {
+		expect(pairwiseDisjoint(empty, setA)).toBe(true);
+	});
+
 	it('any non-empty set and the universal set are not pairwise disjoint', () => {
 		expect(pairwiseDisjoint(setA, universal)).toBe(false);
 	});
 
+	it('the universal set and any non-empty set are not pairwise disjoint', () => {
+		expect(pairwiseDisjoint(universal, setA)).toBe(false);
+	});
+
 	it('the empty set is pairwise disjoint with itself', () => {
 		expect(pairwiseDisjoint(empty, empty)).toBe(true);
 	});

test/unit/comparisons/proper-subset.function.test.ts

@@ -58,10 +58,18 @@ function properSubsetTests<T>(testSets: TestSets<T>): void {
 		expect(properSubset(setA, empty)).toBe(false);
 	});
 
+	it('the empty set is a proper subset of any non-empty set', () => {
+		expect(properSubset(empty, setA)).toBe(true);
+	});
+
 	it('any non-universal set is a proper subset of the universal set', () => {
 		expect(properSubset(setA, universal)).toBe(true);
 	});
 
+	it('the universal set is not a proper subset of any non-universal set', () => {
+		expect(properSubset(universal, setA)).toBe(false);
+	});
+
 	it('the empty set is not a proper subset of itself', () => {
 		expect(properSubset(empty, empty)).toBe(false);
 	});

test/unit/comparisons/proper-superset.function.test.ts

@@ -58,10 +58,18 @@ function properSupersetTests<T>(testSets: TestSets<T>): void {
 		expect(properSuperset(setA, empty)).toBe(true);
 	});
 
+	it('the empty set is not a proper superset of any non-empty set', () => {
+		expect(properSuperset(empty, setA)).toBe(false);
+	});
+
 	it('any non-universal set is not a proper superset of the universal set', () => {
 		expect(properSuperset(setA, universal)).toBe(false);
 	});
 
+	it('the universal set is a proper superset of any non-universal set', () => {
+		expect(properSuperset(universal, setA)).toBe(true);
+	});
+
 	it('the empty set is not a proper superset of itself', () => {
 		expect(properSuperset(empty, empty)).toBe(false);
 	});

test/unit/comparisons/subset.function.test.ts

@@ -58,10 +58,18 @@ function subsetTests<T>(testSets: TestSets<T>): void {
 		expect(subset(setA, empty)).toBe(false);
 	});
 
+	it('the empty set is a subset of any non-empty set', () => {
+		expect(subset(empty, setA)).toBe(true);
+	});
+
 	it('any non-universal set is a subset of the universal set', () => {
 		expect(subset(setA, universal)).toBe(true);
 	});
 
+	it('the universal set is not a subset of any non-universal set', () => {
+		expect(subset(universal, setA)).toBe(false);
+	});
+
 	it('the empty set is a subset of itself', () => {
 		expect(subset(empty, empty)).toBe(true);
 	});

test/unit/comparisons/superset.function.test.ts

@@ -58,10 +58,18 @@ function supersetTests<T>(testSets: TestSets<T>): void {
 		expect(superset(setA, empty)).toBe(true);
 	});
 
+	it('the empty set is not a superset of any non-empty set', () => {
+		expect(superset(empty, setA)).toBe(false);
+	});
+
 	it('any non-universal set is not a superset of the universal set', () => {
 		expect(superset(setA, universal)).toBe(false);
 	});
 
+	it('the universal set is a superset of any non-universal set', () => {
+		expect(superset(universal, setA)).toBe(true);
+	});
+
 	it('the empty set is a superset of itself', () => {
 		expect(superset(empty, empty)).toBe(true);
 	});

test/unit/operations/difference.function.test.ts

@@ -8,9 +8,10 @@ describe('difference', () => {
 });
 
 function differenceTests<T>(testSets: TestSets<T>): void {
-	const { c, e, empty, setA, setB, setC, setD, setE, setF, universal } = testSets;
+	const { c, d, e, empty, f, g, h, i, j, setA, setB, setC, setD, setE, setF, universal } = testSets;
 	const differenceAB = new Set<T>([ c, e ]);
 	const differenceABC = new Set<T>([ e ]);
+	const differenceUA = new Set<T>([ d, f, g, h, i, j ]);
 
 	it('no sets difference returns empty set', () => {
 		const result = difference();
@@ -67,17 +68,27 @@ function differenceTests<T>(testSets: TestSets<T>): void {
 		expect(equivalence(result, setF)).toBe(true);
 	});
 
-	it('any sets\' difference with the empty set is itself', () => {
+	it('any non-empty set\'s difference with the empty set is itself', () => {
 		const result = difference(setA, empty);
 		expect(equivalence(result, setA)).toBe(true);
 	});
 
-	it('any sets\' difference with the universal set is the empty set', () => {
+	it('the empty set\'s difference with any non-empty set is the empty set', () => {
+		const result = difference(empty, setA);
+		expect(equivalence(result, empty)).toBe(true);
+	});
+
+	it('any set\'s difference with the universal set is the empty set', () => {
 		const result = difference(setA, universal);
 		expect(equivalence(result, empty)).toBe(true);
 	});
 
-	it('the empty sets\' difference with itself is itself', () => {
+	it('the universal set\'s difference with any non-universal set contains all elements not in that set', () => {
+		const result = difference(universal, setA);
+		expect(equivalence(result, differenceUA)).toBe(true);
+	});
+
+	it('the empty set\'s difference with itself is itself', () => {
 		const result = difference(empty, empty);
 		expect(equivalence(result, empty)).toBe(true);
 	});

test/unit/operations/intersection.function.test.ts

@@ -67,17 +67,27 @@ function intersectionTests<T>(testSets: TestSets<T>): void {
 		expect(equivalence(result, empty)).toBe(true);
 	});
 
-	it('any sets\' intersection with the empty set is the empty set', () => {
+	it('any non-empty set\'s intersection with the empty set is the empty set', () => {
 		const result = intersection(setA, empty);
 		expect(equivalence(result, empty)).toBe(true);
 	});
 
-	it('any sets\' intersection with the universal set is itself', () => {
+	it('the empty set\'s intersection with any non-empty sets is the empty set', () => {
+		const result = intersection(empty, setA);
+		expect(equivalence(result, empty)).toBe(true);
+	});
+
+	it('any non-universal set\'s intersection with the universal set is itself', () => {
 		const result = intersection(setA, universal);
 		expect(equivalence(result, setA)).toBe(true);
 	});
 
-	it('the empty sets\' intersection with itself is itself', () => {
+	it('the universal set\'s intersection with any non-universal set is that set', () => {
+		const result = intersection(universal, setA);
+		expect(equivalence(result, setA)).toBe(true);
+	});
+
+	it('the empty set\'s intersection with itself is itself', () => {
 		const result = intersection(empty, empty);
 		expect(equivalence(result, empty)).toBe(true);
 	});

test/unit/operations/union.function.test.ts

@@ -69,17 +69,27 @@ function unionTests<T>(testSets: TestSets<T>): void {
 		expect(equivalence(result, universal)).toBe(true);
 	});
 
-	it('any sets\' union with the empty set is itself', () => {
+	it('any non-empty set\'s union with the empty set is itself', () => {
 		const result = union(setA, empty);
 		expect(equivalence(result, setA)).toBe(true);
 	});
 
-	it('any sets\' union with the universal set is the universal set', () => {
+	it('the empty set\'s union with any non-empty set is that set', () => {
+		const result = union(empty, setA);
+		expect(equivalence(result, setA)).toBe(true);
+	});
+
+	it('any non-universal set\'s union with the universal set is the universal set', () => {
 		const result = union(setA, universal);
 		expect(equivalence(result, universal)).toBe(true);
 	});
 
-	it('the empty sets\' union with itself is itself', () => {
+	it('the universal set\'s union with any non-universal set is the universal set', () => {
+		const result = union(universal, setA);
+		expect(equivalence(result, universal)).toBe(true);
+	});
+
+	it('the empty set\'s union with itself is itself', () => {
 		const result = union(empty, empty);
 		expect(equivalence(result, empty)).toBe(true);
 	});

test/unit/operations/xor.function.test.ts

@@ -71,17 +71,27 @@ function xorTests<T>(testSets: TestSets<T>): void {
 		expect(equivalence(result, xorABCDEF)).toBe(true);
 	});
 
-	it('any non-empty sets\' xor with the empty set is itself', () => {
+	it('any non-empty set\'s xor with the empty set is itself', () => {
 		const result = xor(setA, empty);
 		expect(equivalence(result, setA)).toBe(true);
 	});
 
-	it('any non-universal sets\' xor with the universal set is the difference of the universal set and itself', () => {
+	it('the empty set\'s xor with any non-empty set is that set', () => {
+		const result = xor(empty, setA);
+		expect(equivalence(result, setA)).toBe(true);
+	});
+
+	it('any non-universal set\'s xor with the universal set is the difference of the universal set and itself', () => {
 		const result = xor(setA, universal);
 		expect(equivalence(result, xorAU)).toBe(true);
 	});
 
-	it('the empty sets\' xor with itself is itself', () => {
+	it('the universal set\'s xor with any non-universal set is the difference of the universal set and that set', () => {
+		const result = xor(universal, setA);
+		expect(equivalence(result, xorAU)).toBe(true);
+	});
+
+	it('the empty set\'s xor with itself is itself', () => {
 		const result = xor(empty, empty);
 		expect(equivalence(result, empty)).toBe(true);
 	});