The following figure consists of 7 horizontal lines and 13 v

The following figure consists of 7 horizontal lines and 13 vertical lines. The goal of this problem is to count the number of rectangles (squares are a kind of rectangle, but line segments are not). Let V be the set of ail sets of two vertical lines, and let H be the set of ail sets of two horizontal lines. Let R be the set of ail rectangles in the figure. Define a function f: R rightarrow V times H by Explain why f is one-to-one. The function f is one-to-one because vertical lines and horizontal lines determine a unique rectangle.

Solution

function is one-to-one because for every set of 2 horizontal line and a set of 2 vertical lines make a unique rectangle.