To answer this question, first, we need to understand the concept of an inverse operation, especially in the context of binary operations. A binary operation is a calculation that combines two elements to produce another element. Common binary operations are addition, subtraction, multiplication, and division in mathematics.
The inverse of a binary operation, denoted here as x y, is an operation, which when performed after the initial operation, returns the original value. This means, if we take x and y to produce z through the operation x y (denoted as x y -> z), the inverse operation will bring us back to the original x or y value. In mathematical terms, if we perform z (inverse) x operation, it should give us y, and z (inverse) y should return x.
From the given options, we can clearly observe that only one option obeys the rules of the inverse operation, that is 'yx' (option 3). Because only 'yx' will satisfy, z(inverse) x = y and z (inverse) y = x.
So, option 3, 'yx' is the inverse operation of x y in the sense of the inverse element.
Answer:yx