Exercise · ZW-CARTESIAN-PRODUCT-009 · ★★★ Advanced
Select the only pair that belongs to \({1,2} \times \{a,b\}\).
Choose one option.
Show answer
- D. (2,b)
Explanation
In \({1,2} \times \{a,b\}\) the first coordinate comes from \(\{1,2\}\) and the second from \(\{a,b\}\): (2, b) meets both. (3, b) has 3 outside \(\{1,2\}\), (b, 2) has the order reversed, and (1, 2) has the second coordinate outside \(\{a,b\}\).
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
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- 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?
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- 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)?