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A network containing switches is equivalent to a number of networks that differ in the values of their components, in the arrangement of the components, or in both respects. When analyzing or synthesizing such a network, one may treat each different network by itself, and then combine the results. This paper describes a method by which the different aspects of a switchable network may be treated simultaneously. The mathematics by which the network is treated is a combination of ordinary field algebra (complex numbers) and Boolean algebra. The mathematical foundation is first laid out, then interpreted in terms of switchable network elements. The paper is concluded with some examples of analysis and synthesis of switchable networks.