Question

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

• A. $\left\{\right(1,a),(1,b),(2,a),(b,b\left)\right\}$
• B. $\left\{\right(1,1),(2,2),(a,a),(b,b\left)\right\}$
• C. $\left\{\right(1,a),(2,a),(1,b),(2,b\left)\right\}$
• D. $\left\{\right(1,1),(a,a),(2,a),(1,b\left)\right\}$

Answer 1

Answer: (C)

$\left\{\right(1,a),(2,a),(1,b),(2,b\left)\right\}$

If $A$ and $B$ are two non empty sets, then the Cartesian product $A\times B$ is set of all ordered pairs $(a,b)$ such that $a\in A$ and $b\in B$.

Given $A=\{1,2\}$ and $B=\{a,b\}$

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