What is the Cartesian product of set A and set B, if the set A = {1, 2} and set B = {a, b}?

Step 1 (Definition of Cartesian Product): The Cartesian product of set $A$ and set $B$, denoted by $A\times B$, is the set of all ordered pairs $(x,y)$ such that $x\in A$ and $y\in B$.

Step 2 (Form the Pairs): We are given $A=\{1,2\}$ and $B=\{a,b\}$. We match each element of $A$ with each element of $B$:

• For $1\in A$: $(1,a)$ and $(1,b)$

• For $2\in A$: $(2,a)$ and $(2,b)$

Step 3 (Conclusion): The Cartesian product set is: