Express each of these system specifications using predicates, quantifiers, and logical connectives. a) When there is less than 30 megabytes free on the hard disk, a warning message is sent to all users. b) No directories in the file system can be opened and no files can be closed when system errors have been detected. c) The file system cannot be backed up if there is a user currently logged on. d) Video on demand can be delivered when there are at least 8 megabytes of memory available and the connection speed is at least 56 kilobits per second.

Acolor class has three public, integer-returning accessor methods: getred, getgreen, and getblue, and three protected, void-returning mutator methods: setred, setgreen, setblue, each of which accepts an integer parameter and assigns it to the corresponding color component. the class, alphachannelcolor-- a subclass of color-- has an integer instance variable, alpha, containing the alpha channel value, representing the degree of transparency of the color. alphachannelcolor also has a method named dissolve (void-returning, and no parameters), that causes the color to fade a bit. it does this by incrementing (by 1) all three color components (using the above accessor and mutator methods) as well as the alpha component value. write the dissolve method.