Let P[1 . . . n, 1 . . . m] be a 2-dimensional array of the pixels of a black-and-white image:…

 

Let P[1 . . . n, 1 . . . m] be a 2-dimensional array of the pixels of a black-and-white image: for every x and y, the value of P[x, y] = 0 if the hx, yith pixel is black, and P[x, y] = 1 if it’s white. Translate these statements into predicate logic

1. Every pixel in the image is black.

2. There is at least one white pixel.

3. Every row has at least one white pixel.

4.There are never two consecutive white pixels in the same column.

 

A standard American crossword puzzle is a 15-by-15 grid, which can be represented as a two-dimensional 15- by-15 array G, where G[i, j] = True if and only if the cell in the ith row and jth column is “open” (a.k.a. unfilled, a.k.a. not a black square). Maximal contiguous horizontal or vertical sequences of two or more open squares are called words. For any i ≤ 0, i > 15, j ≤ 0, or j > 15, treat G[i, j] = False.

 

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