The set D = {b,c, d,l,n,p, s, w} consists of the eight dogs Bingley, Cardie, Duncan,...

The set D = {b,c, d,l,n,p, s, w} consists of the eight dogs Bingley, Cardie, Duncan, Lily, Nico, Pushkin, Scout, and Whistle. There are three subsets B={d,l,n,s}, F = {c,l,p,s}. and R = {c,n,s,w} of black dogs, female dogs, and retrievers respectively.
(a) Suppose x is one of the dogs in D. Indicate how you can determine which dog x is by asking three yes-or-no questions about x.
(b) Define six subsets of the naturals {1,. .., 64}, each containing 32 numbers, such that you can determine any number n from the answers to the six membership questions for these sets.

(c) (harder) Is it possible to solve part (a) using three sets of dogs that do not have four elements each? What about part (b), with six sets that do not have 32 elements each? Explain your answer.

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Colby Messinger answered 1 year ago

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