public function testUnion()
{
$set1 = new Set(array(1, 2, 3));
$set2 = new Set(array(2, 3, 4));
$set3 = $set1->union($set2);
$arr = array(1, 2, 3, 4);
foreach ($arr as $n) {
self::assertTrue($set3->member($n));
}
}
/**
* Set symmetric difference operator.
*
* Returns a Set which is the symmetric difference of this Set with the
* passed Set.
*
* @param Value $set
*
* @return Set
*/
public function symmetricDifference(Value $set)
{
$returnValue = new Set(array());
return $returnValue->union($this->complement($set), $set->getSet()->complement($this));
}
/**
* Axiom: (A ∪ B) × C = (A × C) ∪ (B × C)
* A union B cross C is the union of A cross C and B cross C
* @dataProvider dataProviderForThreeSets
*/
public function testAUnsionBCrossCEqualsUnsionOfACRossCAndBCrossC(Set $A, Set $B, Set $C)
{
$⟮A∪B⟯×C = $A->union($B)->cartesianProduct($C);
$⟮A×C⟯∪⟮B×C⟯ = $A->cartesianProduct($C)->union($B->cartesianProduct($C));
$this->assertEquals($⟮A∪B⟯×C, $⟮A×C⟯∪⟮B×C⟯);
$this->assertEquals($⟮A∪B⟯×C->asArray(), $⟮A×C⟯∪⟮B×C⟯->asArray());
}
public static function successor($x)
{
return Set::union($x, Set::singleton($x));
}