Question

If A={1,2} , B={a,b} find AXB?

Answer 1

{(1,a)(1,b)(2,a)(2,b)}

Answer 2

Concept:

Set is any collection of objects (elements), which can be mathematical (e.g., numbers and functions) or not. a group is usually represented as an inventory of all its members enclosed in braces or it says that a collection could be a collection of elements or numbers or objects, represented within the curly brackets.

Given:

We are on the condition that $A=\{1,2\}$ and $B=\{a,b\}$.

Find:

we have to search out $A\times B$.

Solution:

For any two non-empty sets $A$ and $B,$ we have

$A\times B=\{(a,b)|a\in A\text{ and }b\in B\}$ and $B\times A=\{(b,a)|a\in A\text{ and }b\in B\}$

Here,  $A=\{1,2\}$ and $B=\{a,b\}$.

Now, we are going to find $A\times B$ using the two non-empty sets of  $A$ and $B,$

We will use the method $A\times B=\{(a,b)|a\in A\text{ and }b\in B\}$, we get

$A\times B=\{(1,a),(1,b),(2,a),(2,b)\}$

Hence, $A\times B$ is $\{(1,a),(1,b),(2,a),(2,b)\}$ when $A=\{1,2\}$ and $B=\{a,b\}$.

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