Cartesian product of any two sets is commutative.Group startsTrue or FalseTrue, unselectedFalse, unselected

Statement Analysis

The Cartesian product of two sets $A$ and $B$, denoted as $A \times B$, is defined as the set of all ordered pairs $(a, b)$ where $a$ is in $A$ and $b$ is in $B$. So,

$A \times B = \{ (a, b) \mid a \in A, b \in B \}$

Similarly, the Cartesian product $B \times A$ is defined as:

$B \times A = \{ (b, a) \mid b \in B, a \in A \}$

Commutative Property Check

The question asks if the Cartesian product is commutative. For a mathematical operation to be commutative, it must satisfy the condition:

$X \times Y = Y \times X$

In this case, we can see that:

• $A \times B$ results in ordered pairs of the form $(a, b)$
• $B \times A$ results in ordered pairs of the form $(b, a)$

Conclusion

Since the ordered pairs are not the same (because the order of elements matters in ordered pairs), we conclude that the Cartesian product is not commutative:

Final Answer: The statement is False.