**Question:**

Let $A=\{-2,2\}$ and $B=(0,3,5)$. Find:

(i) $A \times B$

(ii) $\mathbf{B} \times \mathbf{A}$

(iii) $\mathbf{A} \times \mathbf{A}$

(iv) $\mathbf{B} \times \mathbf{B}$

**Solution:**

(i) Given: $A=\{-2,2\}$ and $B=\{0,3,5\}$

To find: A × B

By the definition of the Cartesian product,

Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.

$P \times Q=\{(p, q): p \in P, q \in Q\}$

Here, $A=\{-2,2\}$ and $B=\{0,3,5\}$. So,

$A \times B=\{(-2,0),(-2,3),(-2,5),(2,0),(2,3),(2,5)\}$

(ii) Given: $A=\{-2,2\}$ and $B=\{0,3,5\}$

To find: $B \times A$

By the definition of the Cartesian product,

Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.

$P \times Q=\{(p, q): p \in P, q \in Q\}$

Here, $A=\{-2,2\}$ and $B=\{0,3,5\}$. So,

$B \times A=\{(0,-2),(0,2),(3,-2),(3,2),(5,-2),(5,2)\}$

(iii) Given: $A=\{-2,2\}$

To find: $A \times A$

By the definition of the Cartesian product,

Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.

$P \times Q=\{(p, q): p \in P, q \in Q\}$

Here, $A=\{-2,2\}$ and $A=\{-2,2\}$.So,

$A \times A=\{(-2,-2),(-2,2),(2,-2),(2,2)\}$

(iv) Given: $B=\{0,3,5\}$

To find: $B \times B$

By the definition of the Cartesian product,

$P \times Q=\{(p, q): p \in P, q \in Q\}$

Here, $B=\{0,3,5\}$ and $B=\{0,3,5\}$. So,

$B \times B=\{(0,0),(0,3),(0,5),(3,0),(3,3),(3,5),(5,0),(5,3),(5,5)\}$