Problem

Let \( A = \{1, 2\} \) and \( B = \{3, 4\} \). Find the Cartesian product \( A \times B \).

Answer

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Answer

Substitute the values of set A and set B into the formula, we get \( A \times B = \{(1, 3), (1, 4), (2, 3), (2, 4)\} \).

Steps

Step 1 ：The Cartesian product of two sets \( A \) and \( B \), denoted by \( A \times B \), is the set of all ordered pairs \((a, b)\) where \(a \in A\) and \(b \in B\).

Step 2 ：So, the Cartesian product \( A \times B \) is \( \{(a, b): a \in A, b \in B\} \).

Step 3 ：Substitute the values of set A and set B into the formula, we get \( A \times B = \{(1, 3), (1, 4), (2, 3), (2, 4)\} \).

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