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Like hardware, we cannot touch software. Without software our computer is quite useless. Software is commonly divided into two types.
The first type of software is used to operate the computer. Operating system is the software which lies in this category. Windows is an operating system. Besides Windows, there are some others operating systems but Windows is very popular. Without any operating system our computer cannot work at all.
The other types of software are nothing to do with the working of computer at all. These are known as programs.
What governs the verb is "first type" [singular] and "other types" [plural] - so you have them correctly.