Exercise · ZW-CARTESIAN-PRODUCT-004 · ★☆☆ Basic
In general, do (a,b) and (b,a) represent the same pair?
Choose one option.
Show answer
- A. No; order matters
Explanation
In an ordered pair order matters: (a, b) = (b, a) only if a = b. For example, (1, 2) ≠ (2, 1).
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-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\.