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Very briefly, electrical engineering deals with the study of the behavior and design of electrical circuits. These circuits include everything from high-voltage power lines to low-voltage electronic circuits like your cell phone.
Computer engineering deals with the study of hardware and software that is an integral part of computer systems.
Software engineering is a related branch of computer engineering in which you'll learn the role software plays in any microprocessor based system.
Nowadays, you have a microprocessor (and therefore software) in almost every appliance at home (dishwashers, washing machines), cars, cell phones, laptops, tablets etc. Ultimately these devices, which make our lives so much easier and fun, rely on good software. It's hard to answer your question briefly, so if you have further specific questions, please feel free to contact me.