1. Let A be the set {e, f, g, h} and B be the set {e,...
1. Let A be the set {e, f, g, h} and B be the set {e, g,
h}.
a. Is A a subset of B?
b. Is B a subset of A?
c. What is A Ս B?
d. What is A x B?
e. What is the power set of B?
2. Determine whether these statements are true or false?
a. ∅ ∈ {∅}
b. {∅} ∈ {∅}
c. {∅} ⊂ {∅, {∅}}
d. ∅ ∈ {∅, {∅}}
e. ∅ ∈ {∅, {∅}, { } }
3. Find the power set of each of these sets, where a and b are
distinct elements.
a. {a}
b. {a, b}
c. {{∅, {∅}}
d. {∅}
e. {∅, { }}
4. What is the cardinality of each of these sets?
a. {a}
b. {a, {a}}
c. {{a}}
d. {a, {a}, {a, {a}}
e. {a, {∅}, {a}}
Homework Answers
#4 ,0, C, d, e, f,g, h}. (a) Using these elements, construct two sets A and...
#4
,0, C, d, e, f,g, h}. (a) Using these elements, construct two sets A and B satisfying | A=5, |B| = 4 and |An Bl 2 (b) Using the sets you chose, compute An B| 4. Let A {r : -1 < x < 1}, B = {x : -2 < x < 2}and C = {x : -2 < x < 3}, where xER. Determine whether the following statements are true or false. (a) AC B (b) C...
1. Consider the sets: A = {a, b, c, d, e, f, h, j}, B =...
1. Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U = {a,b,c,d,e,f,g, h,i,j} a. Draw a Venn diagram and place each element in its appropriate region. Insert a photo of your diagram into your HW document. b. Is C a subset of A? Why? C. Is C a subset of B? Why? d. Is A a subset of B? Why? e. Are B and...
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g}...
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...
Let X be a finite set and F a family of subsets of X such that...
Let X be a finite set and F a family of subsets of X such that every element of X appears in at least one subset in F. We say that a subset C of F is a set cover for X if X =U SEC S (that is, the union of the sets in C is X). The cardinality of a set cover C is the number of elements in C. (Note that an element of C is a...
Let U ={a, b, c, d, e, f, g, h, i, j, k}. Let A={d, f,...
Let U ={a, b, c, d, e, f, g, h, i, j, k}. Let A={d, f, g, h, i, k}. Let B={a, d, f, g, h}. Let C={a, c, f. i, k} Determine (AUC) U ( AB). Choose the correct answer below and, if necessary, fill in the answer box in your choice. OA. (AUC) U(ANB)= } (Use a comma to separate answers as needed.) OB. (A'UC) U (ANB) is the empty set. LE This Question: 1 pt Let U={x|XEN...
Program has to be in C# language Write a computer program that takes two sets (let...
Program has to be in C# language
Write a computer program that takes two sets (let the user determine the cardinality of each set and enter them manually) and calculates the following operations: Union Intersection Difference (set1 - set2) Cartesian product (set2 X set1) Check whether set2 is a subset of set1 or set1 is a subset of set2 Find the powerset of set1 and print out its elements and cardinality
Question4 please (1). Let f: Z → Z be given by f(x) = x2. Find F-1(D)...
Question4 please
(1). Let f: Z → Z be given by f(x) = x2. Find F-1(D) where (a) D = {2,4,6,8, 10, 12, 14, 16}. (b) D={-9, -4,0, 16, 25}. (c) D is the set of prime numbers. (d) D = {2k|k Ew} (So D is the set of non-negative integer powers of 2). (2). Suppose that A and B are sets, C is a proper subset of A and F: A + B is a 1-1 function. Show that...
discrete math '-(oe : length(a) 29, be the alphabet {a,b,c,d,e,f,g) and let 7. Let a) How many elements are in the following set? {ωΣ: no letter in ω is used more than once) b) Find the proba...
discrete math
'-(oe : length(a) 29, be the alphabet {a,b,c,d,e,f,g) and let 7. Let a) How many elements are in the following set? {ωΣ: no letter in ω is used more than once) b) Find the probability that a random word we has al distinct letters. e) Find the probability that a random word oe has the letter g used exactly once. d) Find the probability that a random word e does not contain the letter g.
'-(oe : length(a)...
MOREHOUSE COLLEGE DEPARTMENT OF MATHEMATICS MATH 255 Set Theory WORKSHEET 2 . Let A (ak (el)...
MOREHOUSE COLLEGE DEPARTMENT OF MATHEMATICS MATH 255 Set Theory WORKSHEET 2 . Let A (ak (el) B (c0) and C-(ao.).Determine which of the following statements are true or false. (a) ce a (b) (c) e A (e) (e) s A (d) BSA (e) AC B (8) 0 EB (h) AnBSc 2 Let A-(o.be) and B (e.d). Find A-B and B-A, and verify that A-BAB-A 3. Let A-(a,b.c.d.e) and U-fa,he.d.e,1,2.3) (a) Find A (b) Find A-U c Find u-A (d) Find...
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets...
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
#4
,0, C, d, e, f,g, h}. (a) Using these elements, construct two sets A and B satisfying | A=5, |B| = 4 and |An Bl 2 (b) Using the sets you chose, compute An B| 4. Let A {r : -1 < x < 1}, B = {x : -2 < x < 2}and C = {x : -2 < x < 3}, where xER. Determine whether the following statements are true or false. (a) AC B (b) C...
1. Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U = {a,b,c,d,e,f,g, h,i,j} a. Draw a Venn diagram and place each element in its appropriate region. Insert a photo of your diagram into your HW document. b. Is C a subset of A? Why? C. Is C a subset of B? Why? d. Is A a subset of B? Why? e. Are B and...
Let U ={a, b, c, d, e, f, g, h, i, j, k}. Let A={d, f, g, h, i, k}. Let B={a, d, f, g, h}. Let C={a, c, f. i, k} Determine (AUC) U ( AB). Choose the correct answer below and, if necessary, fill in the answer box in your choice. OA. (AUC) U(ANB)= } (Use a comma to separate answers as needed.) OB. (A'UC) U (ANB) is the empty set. LE This Question: 1 pt Let U={x|XEN...
Program has to be in C# language
Write a computer program that takes two sets (let the user determine the cardinality of each set and enter them manually) and calculates the following operations: Union Intersection Difference (set1 - set2) Cartesian product (set2 X set1) Check whether set2 is a subset of set1 or set1 is a subset of set2 Find the powerset of set1 and print out its elements and cardinality
Question4 please
(1). Let f: Z → Z be given by f(x) = x2. Find F-1(D) where (a) D = {2,4,6,8, 10, 12, 14, 16}. (b) D={-9, -4,0, 16, 25}. (c) D is the set of prime numbers. (d) D = {2k|k Ew} (So D is the set of non-negative integer powers of 2). (2). Suppose that A and B are sets, C is a proper subset of A and F: A + B is a 1-1 function. Show that...
discrete math
'-(oe : length(a) 29, be the alphabet {a,b,c,d,e,f,g) and let 7. Let a) How many elements are in the following set? {ωΣ: no letter in ω is used more than once) b) Find the probability that a random word we has al distinct letters. e) Find the probability that a random word oe has the letter g used exactly once. d) Find the probability that a random word e does not contain the letter g.
'-(oe : length(a)...
MOREHOUSE COLLEGE DEPARTMENT OF MATHEMATICS MATH 255 Set Theory WORKSHEET 2 . Let A (ak (el) B (c0) and C-(ao.).Determine which of the following statements are true or false. (a) ce a (b) (c) e A (e) (e) s A (d) BSA (e) AC B (8) 0 EB (h) AnBSc 2 Let A-(o.be) and B (e.d). Find A-B and B-A, and verify that A-BAB-A 3. Let A-(a,b.c.d.e) and U-fa,he.d.e,1,2.3) (a) Find A (b) Find A-U c Find u-A (d) Find...
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
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