Kenneth Rosen Edition 7 Exercise 2.1 Question 27 (Page No. 126)

Question

Let $A = \left \{ a,b,c,d \right \}$ and $B= \left \{ y,z\right \}$ Find

1. $A \times B.$
2. $B \times A.$

Answer 1

$A=\left\{a,b,c,d\right\}$

$B=\left\{y,z\right\}$

1. $A \times B=\left\{(a,y),(a,z),(b,y),(b,z),(c,y),(c,z),(d,y),(d,z)\right\}$
2. $B\times A=\left\{(y,a),(z,a),(y,b),(z,b),(y,c),(z,c),(y,d),(z,d)\right\}$

The above operation performed on set $A, B$ is called Cartesian product, which is defined as:

$A\times B=\left\{(a,b)\mid a \in A \land b\in B\right\}$