For each of the following language descriptions, give a regular expression that matches exactly that language. You don't have to find the shortest possible regular expression. You may use expressions such as [a z] to represent the letters a through z, and/or regular definitions: letter + [a z] string + letter* To make things clearer, use to mean a single space (e.g. write "Hello world" instead of "Hello world".) (a) Strings over the alphabet {a,b,c,d} that are in alphabetical order. Examples: aabccc, abcd, bd, a, ad Not examples: dc, ca, cba (b) Natural numbers (0 and up), with no leading zero unless the whole thing is a single zero, and going right-to-left, groups of 3 digits are separated by commas. Examples: 0; 1; 12; 123; 1,234; 12,345; 1,000,000 Not examples: 01; 1000; 123,4; 12,34 (c) Strings consisting of letters a-z and spaces that do not begin or end with whitespace and all white space is one space long. Example: "so this is ok" Not examples: "this " this too", "and this " is bad