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Unformatted text preview: P roblem 1.17 LP L R I K SENGUPTA The function symbol that I am using is height(x), which takes one argument x the name of a person whose height is being compared. The relation symbols "<" and "=" are used in their usual context, i.e. < refers to less than, and = refers to equal to. Each of these last two symbols takes two arguments p and q and compares them. This combination of a unary function symbol and two binary relation symbols allows us to compare the heights of any two people, who serve as the arguments for the function symbols. We use < (height(x), height(y)) to express the height of x is less than the height of y, thereby comparing the heights of our subjects x and y, and concluding that y is taller than x. Similarly, we use = (height(z), height(w)) to express the height of z is equal to the height of w, thereby comparing the heights of our subjects z and w, and concluding that z and w have the same height. So in my language, the answers are: 1. < (height(Sam), height(George)) George is taller than Sam. 2. = (height(Sam), height(Mary)) Sam and Mary are the same height. The only problem we run into is that complex functions are impossible to conceive. For instance, the following expression is undefined: height(height(Sam)) Because the "height of the height of Sam" doesn't make any sense. So it is impossible to form complex composite functions when we use my notation. ...
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