Cartesian Product Flashcards
1
Q
What is the Cartesian product of two sets?
A
The Cartesian product of two sets A and B is the set of ordered pairs of the elements contained in A and B. That is—
A × B = {(x,y): x ∈ A, y ∈ B}
2
Q
What are the properties of the Cartesian Product
A
If A and B are non-empty sets, then:
1. A × B ≠ B × A
2. A × Φ = Φ where Φ is an empty set
3. If n(A) = M and n(B) = N, then n(A × B) = MN
4. A × (B × C) ≠ (A × B) × C
5. A × (B ∩ C) = (A × B) ∩ (A × C)
6. A × (B U C) = (A × B) U (A × C)
7. A × B = B × A if A or B = Φ
3
Q
What is the cardinality of a Cartesian product?
A
It is the total number of ordered pairs formed by the Cartesian product of two or more sets.
