Exercise · ZW-CARTESIAN-PRODUCT-008 · ★★☆ Intermediate
When is (a,b) = (c,d)?
Choose one option.
Show answer
- A. When a=c and b=d
Explanation
Two ordered pairs are equal when they coincide coordinate by coordinate: (a, b) = (c, d) if and only if a = c and b = d.
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-009 Select the only pair that belongs to 1,2 × \a,b\.