Exercise · ZW-CARTESIAN-PRODUCT-005 · ★☆☆ Basic
What happens with A × ∅?
Choose one option.
Show answer
- D. It is ∅
Explanation
To form a pair of A × ∅ we would have to choose an element of ∅, and there is none. So A × ∅ = ∅ (and also ∅ × A = ∅). It is consistent with |A| · 0 = 0.
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-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\.