Question

In: Advanced Math

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.

Solutions

Expert Solution


Related Solutions

An experiment consists of four outcomes (A, B, C, D) with P(A) = 0.2, P(B) =...
An experiment consists of four outcomes (A, B, C, D) with P(A) = 0.2, P(B) = 0.3, and P(C) = 0.4.  The P(D) is 0.500 0.024 0.100 0.900 Given that event E has a probability of 0.3, the probability of the complement of event E cannot be determined with the above information can have any value between zero and one must be 0.7 is 0.3 If P(A) = 0.38, P(B) = 0.83, and P(A Ç B) = 0.57; then P(A È...
Let S = {a, b, c, d} and P(S) its power set. Define the minus binary...
Let S = {a, b, c, d} and P(S) its power set. Define the minus binary operation by A − B = {x ∈ S | x ∈ A but x /∈ B}. Show that (by counter-examples) this binary operation is not associative, and it does not have identity
Let S = {a, b, c}. Draw a graph whose vertex set is P(S) and for...
Let S = {a, b, c}. Draw a graph whose vertex set is P(S) and for which the subsets A and B of S are adjacent if and only if A ⊂ B and |A| = |B| − 1. (a) How many vertices and edges does this graph have? (b) Can you name this graph? (c) Is this graph connected? (d) Does it have a perfect matching? If yes, draw a sketch of the matching. (e) Does it have a...
Assume a competitive market with the following demand and supply curve, D(p) =a-b*P and S(p)= c...
Assume a competitive market with the following demand and supply curve, D(p) =a-b*P and S(p)= c + d*. Assume the government imposes a tax of t on each unit sold. The equilibrium prices without (P) and with the tax (net price Pn and gross price Pg ) are
P(W)= 0.3 P(low/W) = 0.50 P(low/S) = 0.10 P(S)= 0.7 P(medium/W)= 0.40 P(medium/S)= 0.25 P(high/W) =...
P(W)= 0.3 P(low/W) = 0.50 P(low/S) = 0.10 P(S)= 0.7 P(medium/W)= 0.40 P(medium/S)= 0.25 P(high/W) = 0.10 P(high/S) = 0.65 BDSC 340.001-3 d) Construct a decision tree for this problem and analyze it. e) What is McHuffter’s optimal decision? f) What is the expected value of the survey(sample) information?
Let S{a, b, c, d} be a set of four positive integers. If pairs of distinct...
Let S{a, b, c, d} be a set of four positive integers. If pairs of distinct elements of S are added, the following six sums are obtained:5,10, 11,13,14,19. Determine the values of a, b, c, and d. (There are two possibilities. )
Let p be an element in N, and define d _p to be the set of...
Let p be an element in N, and define d _p to be the set of all pairs (l,m) in N×N such that p divides m−l. Show that d_p is an equivalence relation
if A union B = S, A intersect B = empty set, P(A) = x, P(B)...
if A union B = S, A intersect B = empty set, P(A) = x, P(B) = y, and 3x-y = 1/2, find x and y.
Let P(A) = 0.40, P(B) = 0.20, P(C) = 0.50, P(D) = 0.30, P(A ∩ B)...
Let P(A) = 0.40, P(B) = 0.20, P(C) = 0.50, P(D) = 0.30, P(A ∩ B) = 0.15, P(A | C) = 0.60, P(B | C) = 0.20, P(B ∩ D) = 0.10, and C and D are mutually exclusive. Find ... a. P(C ∩ D) b. P(C U D) c. P(B ∩ C) d. Which one of the following pairs is a pair of statistically independent events? (A and C) (B and D) (B and C) (C and D)
Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a...
Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a field
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT