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Chapter 0: Q4E (page 26)

If Ahasa elements andB hasb elements, how many elements are inA脳B? Explain your answer.

Short Answer

Expert verified

A脳Bmeans you need to find out the cartesian product of setsA andB . So, the product ofA脳Bhasa脳bnumber of elements in it.

Step by step solution

01

Define the Cartesian Product

The Cartesian Product of setsAandBis defined as the set of all ordered pairs(x,y)such thatxbelongs toAandybelongs toB.

02

Describe a method to obtain the Cartesian Product

For example, ifA={1,2} , andB={3,4,5}, then the Cartesian Product ofsetsAandBis{(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)} .One of the methods of constructing the Cartesian product is to select an element ofA(xa)and pair it with each and every element ofB(y1,y2,...,yb). This produces the pairings{(x1,y1),(x1,y2),...,(x1,yb)}

On repeating this procedure for each remaining element for finding the number of elements, multiply the elements in set A and set B.

Thus, the number of elements in A脳Bis a脳b.

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