Show that the `F: R ->R` given by `(a , b)->m a x {a , b}`and the `G: R ->R` given by `(a , b) ->min {a , b}`are binary operations.

Explanation

To show that the functions \( F: \mathbb{R} \times \mathbb{R} \to \mathbb{R} \) given by \( F(a, b) = \max\{a, b\} \) and \( G: \mathbb{R} \times \mathbb{R} \to \mathbb{R} \) given by \( G(a, b) = \min\{a, b\} \) are binary operations, we need to verify that for any two real numbers \( a \) and \( b \), the results of these operations also yield a real number.

### Step 1: Show that \( F(a, b) = \max\{a, b\} \) is a binary operation.

1. **Definition of Binary Operation**: A binary operation on a set \( S \) is a function that combines two elements of \( S \) to produce another element of \( S \).

2. **Consider any two real numbers \( a \) and \( b \)**: Since \( a \) and \( b \) are real numbers, we have \( a, b \in \mathbb{R} \).

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