let A={1,3,6,8,9} , B={2,5,6,7,8} , C={1,4,6,7,8,9} , and D={1,2}
a.calculate P(D) i.e power set
b. What is (B ∩ C) x {1,2}
a. P(D) = {{},{1},{2},{1,2}} b. (B ∩ C) x {1,2} = {6,7,8} x {1,2} = {(6,1),(6,2),(7,1),(7,2),(8,1),(8,2)}
let A={1,3,6,8,9} , B={2,5,6,7,8} , C={1,4,6,7,8,9} , and D={1,2} a.calculate P(D) i.e power set b. What...
Let A={1,2,3,4}. Pick a subset B⊆A uniformly among the 2^4 subsets (i.e. the power set ofA) and let X be its size. Then likewise pick a subset C⊆B uniformly from the power set of B and let Y be its size. Give the joint p.m.f of (X, Y) and compute E(X−Y). Hint: X, Y can take value 0 if you pick the empty set. You can either write down a table or a compact expression of the form P(X=i, Y=j).
Let P be the power set of {a, b, c}. A function f: P , the set of integers, follows: For A in P, f(A) = the number of elements in A. 1. Is f one-to-one? Explain. 2. Is f onto? Explain.
5-13 please
Homework on sets 1. let the universe be the set U (1,23. .,1.0), A (147,10), B- (1,2 list the elements for the following sets. a. B'nt C-A) b. B-A c. ΒΔΑ 2. Show that A (3,2,1] and B (1,2,3) are equal 3. Show that X Ixe Rand x > 0 and x < 3j and ( 1,2) are equal. 5. Use a Ven diagram and shade the given set. (cnA)-(B-Arnc) Show that A (x| x3-2x2-x+2 O) is not...
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of these 7 points. We define the following partial order on S: We have (r, y)(', y) iff x< x and y < / Draw the Hasse diagram of S S 6. We consider the same partial order as in Problem 5, but it is now defined on R2....
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: A ∪ B 12. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: b. A ∩ B 13. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: AC...
6. Let X have a N(1,2) distribution. Using only the tables, find: a) P(X 1.5) b) P(-1.1 X < 3.3) c) P(X-.9) d) A point c such that P(X > c) = 01 e) A point d such that P(X < d) 005
Let P(X) be the power set of a non-empty set X. For any two subsets A and B of X, define the relation A B on P(X) to mean that A union B = 0 (the empty set). Justify your answer to each of the following? Isreflexive? Explain. Issymmetric? Explain. Istransitive? Explain.
4. [3 marks] Let R be a relation on a set A. Let A {1,2, 3, X, Y} and R = {(1, 1), (1,3), (2,1), (3, 1), (1, X), (X, Y)} (a) What is the reflexive closure of R? (b) What is the symmetric closure of R? (c) What is the transitive closure of R?
Let the universal set S be S = {1,2,...,10}, and A = {1,2,3}, B = {3,4,5,6,7} and C = {7,8,9,10} 1) Find (A∪C)−B 2) Find A^c ∩(B^c ∪C)
(a) (3 pts) Let A = {1,2,3,4}. Pick a subset B C A uniformly among the 24 subsets (i.e. the power set of A) and let X be its size. Then likewise pick a subset C C B uniformly from the power set of B and let Y be its size. Give the joint p.m.f of (X,Y) and compute E(X – Y). Note: X, Y can take value 0 if you pick the empty set. You can either write down...