Chapter 0: Q4E (page 26)

If $A$ has $a$ elements and $B$ has $b$ elements, how many elements are in $A \times B$ ? Explain your answer.

Short Answer

Expert verified

$A \times B$ means you need to find out the cartesian product of sets $A$ and $B$ . So, the product of $A \times B$ has $a \times b$ number of elements in it.

Step by step solution

Define the Cartesian Product

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

Describe a method to obtain the Cartesian Product

For example, if $A = {1, 2}$ , and $B = {3, 4, 5}$ , 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 of $A (x_{a})$ and pair it with each and every element of $B (y_{1}, y_{2}, ..., y_{b})$ . This produces the pairings ${(x_{1}, y_{1}), (x_{1}, y_{2}), ..., (x_{1}, y_{b})}$

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 $A \times B$ is $a \times b$ .

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If $A$ has $a$ elements and $B$ has $b$ elements, how many elements are in $A \times B$ ? Explain your answer.

Short Answer

Step by step solution

Define the Cartesian Product

Describe a method to obtain the Cartesian Product

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

Short Answer

Step by step solution

Define the Cartesian Product

Describe a method to obtain the Cartesian Product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

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If $A$ has $a$ elements and $B$ has $b$ elements, how many elements are in $A \times B$ ? Explain your answer.