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

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Advance Math

The set D = {b,c, d,l,n,p, s, w} consists of the eight dogsBingley, 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 retrieversrespectively.
(a) Suppose x is one of the dogs in D. Indicate how you candetermine which dog x is by asking three yes-or-no questions aboutx.
(b) Define six subsets of the naturals {1,. .., 64}, eachcontaining 32 numbers, such that you can determine any number nfrom the answers to the six membership questions for thesesets.

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

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