Question

If A = {0,1} and B = {1,0}, then what is $A\times B$ equal to ?

Answer 1

Hint: In this question it is given that if A = {0,1} and B = {1,0}, then we have to find $A\times B$.So to find the solution we need to know that $$A\times B$$ is called the Cartesian product of A and B, and if set A = {a,b} and set B = {1,2,3} then the Cartesian product $$A\times B=\left\{ \left( a,1\right) ,\left( a,2\right) ,\left( a,3\right) ,\left( b,1\right) ,\left( b,2\right) ,\left( b,3\right) \right\} $$........(1)
Complete step-by-step solution:
Given,
A = {0,1} and B = {1,0},
Therefore by equation (1) we can write,
$$A\times B=\left\{ \left( 0,1\right) ,\left( 0,0\right) ,\left( 1,1\right) ,\left( 1,0\right) \right\} $$
Note: While writing the cartesian product you need to know that, each and every element of $A\times B$ is called the ordered pair, i.e (a, b), where ‘a’ is the element of set A and ‘b’ is the element of set B and also the ordered pair (a, b)$\neq$(b, a).