`A times (B cup C)`

Answer

To solve the expression \( A \times (B \cup C) \), we can use the distributive law of set theory. Here’s the step-by-step solution:

### Step 1: Understand the Expression
The expression \( A \times (B \cup C) \) represents the Cartesian product of set \( A \) with the union of sets \( B \) and \( C \).

### Step 2: Apply the Distributive Law
According to the distributive law in set theory, we can distribute the Cartesian product over the union. This means we can rewrite the expression as follows:
\[ A \times (B \cup C) = (A \times B) \cup (A \times C) \]

### Step 3: Write the Final Result
Thus, the final result of the expression \( A \times (B \cup C) \) is:
\[ A \times (B \cup C) = A \times B \cup A \times C \]

### Summary
The expression \( A \times (B \cup C) \) simplifies to \( A \times B \cup A \times C \) using the distributive law.

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