Complexity Explorer Santa Fe Institute

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Vector and Matrix Algebra

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1.4 Boolean Set Operations » Quiz #3 Solution

Question 1: The union of A and B is equal to A, since the elements of B (4 and 5) are already in A.  The complement of A (with respect to universe U) is {8, 9, 10}. 


Question 2: Recall that the Cartesian product B \times Bis a set whose elements consist of all possible two-component pairs from the two sets (here, B and B).   Since B = {4, 5}, we get the set of all possible 2-element pairs using those elements.


Question 3: The elements of  A \times B \times U  are three-component vectors created by taking each element of A for the first component, and for each of those taking each element of B for the second component, and then for each of those, taking each element of U for the third component.  There are 7 possible first components (values from A), times 2 possible second components (values from B), timex 10 possible third components (values from U).  7 times 2 times 10 = 140.