Exercise · ZW-CARTESIAN-PRODUCT-001 · ★☆☆ Basic
What does A × B contain?
Choose one option.
Show answer
- D. Ordered pairs (a,b)
Explanation
A × B is the set of all ordered pairs (a, b) with a ∈ A and b ∈ B. It is neither the union nor a set of loose elements, and the pairs are ordered.
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-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)?
- ZW-CARTESIAN-PRODUCT-009 Select the only pair that belongs to 1,2 × \a,b\.