In black-and-white printing the page image can be represented within a computer as an array of binary values indicating whether or not pixels should be inked. The Boolean operators of AND, OR, and EXCLUSIVE-OR are often used when adding new objects to the image array. For color printing the page may be represented as an array of "continuous-tone" color values, and the generalization of these logic functions to gray-scale or full-color images is, in general, not defined or understood. When incrementally composing a page image, new colors can replace old in an image buffer, or new colors and old can be combined according to some mixing function to form a composite color, which is stored. This paper examines the properties of the Boolean operations and suggests full-color functions thatpreserve the desired properties. These functions can be used to combine colored images in ways that preserve information about object shapes when the shapes overlap. The relationships between the proposed functions and physical models of color mixing are also discussed.