Exercise · ZW-CARTESIAN-PRODUCT-010 · ★★★ Advanced
In general, what is the relation between A × B and B × A?
Choose one option.
Show answer
- C. They are not equal as sets of pairs, although they have the same finite cardinality
Explanation
A × B and B × A have pairs with the coordinates in a different order, so in general they are not the same set. If both are finite they do have the same number of elements, |A| · |B|.
Review the concept: Cartesian product
The Cartesian product of A and B is the set of all ordered pairs whose first coordinate is in A and whose second is in B.
\[A \times B = \{(a,b): a\in A,\ b\in B\}\]
More practice problems: cartesian product
- ZW-CARTESIAN-PRODUCT-001 What does A × B contain?
- ZW-CARTESIAN-PRODUCT-002 If |A| = 2 and |B| = 3, what is |A × B|?
- ZW-CARTESIAN-PRODUCT-003 In (a,b) ∈ A × B, where is a?
- ZW-CARTESIAN-PRODUCT-004 In general, do (a,b) and (b,a) represent the same pair?
- ZW-CARTESIAN-PRODUCT-005 What happens with A × ∅?
- ZW-CARTESIAN-PRODUCT-006 If |A| = 3 and |B| = 2, how many pairs does A × B have?
- ZW-CARTESIAN-PRODUCT-007 If A × B = ∅, then necessarily...
- ZW-CARTESIAN-PRODUCT-008 When is (a,b) = (c,d)?