N-set Diagrams. A computer store offers a basic computer with four options A, B, C, and D,...

N-set Diagrams. A computer store offers a basic computer with four options A, B, C, and D, any or none of which buyers can select.

a. How many different sets of options can buyers choose? For example, one choice is A and C, another choice is no options, and another choice is all options.

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b. Consider the four-circle Venn diagram below. Label the regions with the various sets of options.

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c. Does the diagram in part (b) represent all the sets of options? If not, which sets of options are missing?

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d. Suppose the computer store offered five options A, B, C, D, and E. How many different sets of options would be available?

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e. Generalizing from parts (a–d), how many different sets of options are available if the store offers N options, where N = 2,3,4,..,?