Question

State True or False

Let $A=\{1,2\}$ and $B=\{2,3,4\}$, then A $\times$ B = B $\times$ A ?

• A. True
• B. False

Answer 1

The correct option is B False

Product of two sets is the set of ordered pairs formed by mapping every element from the first set to every element of the second set.
So, $A\times B=$ { $(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)$ }
And $B\times A=$ { $(2,1),(2,2),(3,1),(3,2),(4,1),(4,2)$ }
Clearly, $A\times B\ne B\times A$