1. Let's first understand what a binary operation is. A binary operation on a set is a rule for combining any two elements of the set to form another element of the same set. 2. For example, addition (+) and multiplication (×) on the set of real numbers are binary operations because adding or multiplying any two real numbers results in another real number. 3. Now, consider a multiple choice question: "Which of the following is a binary operation on the set of integers?" 4. Options might be: a) Addition (+) b) Subtraction (-) c) Division (/) d) Exponentiation (^) 5. Let's analyze each: - a) Addition: Adding any two integers results in an integer, so this is a binary operation. - b) Subtraction: Subtracting any two integers results in an integer, so this is also a binary operation. - c) Division: Dividing two integers does not always result in an integer (e.g., 1/2 is not an integer), so this is not a binary operation on integers. - d) Exponentiation: Raising an integer to the power of another integer results in an integer if the exponent is non-negative, but not always if negative exponents are allowed. Typically, exponentiation is not considered a binary operation on integers because it may not be closed. 6. Therefore, the correct answers are a) Addition and b) Subtraction. Final answer: Addition and Subtraction are binary operations on the set of integers.