If A = {5, 7), find (i) A × A × A.

We have, A = {5, 7}

So, 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, $A=\{5,7\}$ and $A=\{5,7\} .$ So,

$A \times A=\{(5,5),(5,7),(7,5),(7,7)\}$

Now again, we apply the definition of Cartesian product to find $A \times A \times A$

Here, $A=\{5,7\}$ and $A \times A=\{(5,5),(5,7),(7,5),(7,7)\}$

$\therefore A \times A \times A=\{(5,5,5),(5,5,7),(5,7,5),(5,7,7),(7,5,5),(7,5,7),(7,7,5),(7,7,7)\}$