Show that (p-q) - (r-s) and (p r)- (g s) are not logically equivalent. the dual of a compound proposition that contains only the logical operators v, ^, and-is the compound proposition obtained by replacing each v by i, each ^ by v, each t by f, and each f by t. the dual of s is denoted by s*

At the county fair, animals are judged for the quality of their breeding and health. the animal pens are arranged in an array, with one animal in each pen. a barn can hold at most 10 rows of pens and at most 6 pens in each row, with room for people to walk around them. what different ways can the planners of the county fair arrange the pens for the horses and cows in the same barn?