Relation and Functions Exercise 1.1 - Q. 2 ) . Let A = {1, 2, 3} and B{ x | x is a prime number less than 10}. Find A X B and B X A

 Q. 2 ) . Let A = {1, 2, 3} and B{ x | x is a prime number less than 10}. Find A X B and B X A

Given the sets $A = \{1, 2, 3\}$ and $B = \{ x \mid x \text{ is a prime number less than 10} \}$, we first need to determine the elements of set $B$.

The prime numbers less than 10 are: 2, 3, 5, and 7. Therefore, $B = \{2, 3, 5, 7\}$.

Next, we will find the Cartesian products $A \times B$ and $B \times A$.

Cartesian Product $A \times B$

The Cartesian product $A \times B$ is the set of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$.

So, we list all possible pairs:

$$A \times B = \{ (1,2), (1,3), (1,5), (1,7), (2,2), (2,3), (2,5), (2,7), (3,2), (3,3), (3,5), (3,7) \}$$

Cartesian Product $B \times A$

Similarly, the Cartesian product $B \times A$ is the set of all ordered pairs $(b, a)$ where $b \in B$ and $a \in A$.

So, we list all possible pairs:

$$B \times A = \{ (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (5,1), (5,2), (5,3), (7,1), (7,2), (7,3) \}$$

Summary

$$A \times B = \{ (1,2), (1,3), (1,5), (1,7), (2,2), (2,3), (2,5), (2,7), (3,2), (3,3), (3,5), (3,7) \}$$

$$B \times A = \{ (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (5,1), (5,2), (5,3), (7,1), (7,2), (7,3) \}$$