Question

Given two sets A and B, the intersection of these sets, denoted A ∩ B, is...

  • Given two sets A and B, the intersection of these sets, denoted A ∩ B, is the set containing the elements that are in both A and B. That is, A ∩ B = {x : x ∈ A and x ∈ B}.
  • Two sets A and B are disjoint if they have no elements in common. That is, if A ∩ B = ∅.
  • Given two sets A and B, the union of these sets, denoted A ∪ B, is the set containing the elements that are either in A or in B (or in both). That is, A ∪ B = {x : x ∈ A or x ∈ B}.
  • Given two sets A and B, the relative complement or difference of these sets, denoted B −A, is the set of elements that are in B but not in A. That is, B − A = {x : x ∈ B and x /∈ A}.

  • Given a universal set U and a set A, the complement of the set A with respect to the set U, denoted as AC or A, is

the set U − A. That is, A = {x ∈ U : x /∈ A}.

  • Given two sets A and B, the symmetric difference of these sets, denoted A ⊕ B, is the set of elements that are in A or B but not both. That is, A ⊕ B = (A ∪ B) − (A ∩ B).
  1. Let A = {a,b,c,d,e,f}, B = {a,c,e,f,g,h,i}, C = {b,c,d,f,g,h} and U = {a,b,c,d,e,f,g,h,i,j}. Express each of the following in roster notation.

              (a) A ∪ B                                                      (b) A ∩ B                                                      (c) A ⊕ B

              (d) A − C                                                       (e) C − A                                                       (f) C

               (g) A − (B ∪ C)                                            (h) A ∪ (B ∩ C)                                (i) (A ∪ B) ∩ (A ∪ C)

  1. Suppose U = {1,2,3,4,5,6} and B = {2,3,4}.
    1. What can you say about the set A if A ∪ B = {1,2,3,4,5}?
    2. What can you say about the set A if A ∩ B = {2,3}?
    3. What can you say about the set A if A ⊕ B = {1,2,4,5}?
  2. What can you day about the sets A and B if A ⊕ B = ∅?
  3. Draw a general Venn diagram representing each of the following:

  1. A ∩ B (b) A − B

               (c) (A ∪ B) − C                                                                                (d) A ∪ (B − C)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Consider the following situation: The universal set U is given by: U = {?|? ?...
1. Consider the following situation: The universal set U is given by: U = {?|? ? ? , ? ≤ 12} A is a proper subset of U, with those numbers that are divisible by 4. B is a proper subset of U, with those numbers that are divisible by 3. C is a proper subset of U, with those numbers that are divisible by 2 a) Using Roster Notation, list the elements of sets U, A, B and C....
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of the following elements: A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x ∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J = R. Consider the relation ∼ on S given...
Discrete Math In this assignment, A, B and C represent sets, g is a function from...
Discrete Math In this assignment, A, B and C represent sets, g is a function from A to B, and f is a function from B to C, and h stands for f composed with g, which goes from A to C. a). Prove that if the first stage of this pipeline, g, fails to be 1-1, then the entire pipeline, h can also not be 1-1. You can prove this directly or contrapositively. b). Prove that if the second...
We denote |S| the number of elements of a set S. (1) Let A and B...
We denote |S| the number of elements of a set S. (1) Let A and B be two finite sets. Show that if A ∩ B = ∅ then A ∪ B is finite and |A ∪ B| = |A| + |B| . Hint: Given two bijections f : A → N|A| and g : B → N|B| , you may consider for instance the function h : A ∪ B → N|A|+|B| defined as h (a) = f (a)...
Consider two data sets, A and B. The sets are identical except that the high value...
Consider two data sets, A and B. The sets are identical except that the high value of data set A is three times greater than the high value of data set B. (a) How do the medians of the two data sets compare? It is impossible to know how the medians compare. Both sets have the same median.    Set A has a higher median. Set B has a higher median. (b) How do the means of the two data sets...
please match the following to their definitions       -       A.       B....
please match the following to their definitions       -       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.    Crude Mortality Rate       -       A.       B.       C.       D.       E.       F.       G.       H.       I.       J.    Cause-specific mortality...
How can the following set of equations be solved using matrices? A+ B + F =...
How can the following set of equations be solved using matrices? A+ B + F = 16 B + C + D = 15 D+ E = 13 H+ I = 14 F+G+H+I = 20 F+ G = 6 A, B,C,D, E, F, G and H are limited to having a unique value. and the values are  1 though 9
Suppose that A and B are two events in a sample space S with P(B)=0.04, P(A...
Suppose that A and B are two events in a sample space S with P(B)=0.04, P(A n B)=0.03 and P(A u B) =0.46 a) what is P(B) complement b)what is P(A) c)what is P( AUB) complement d)what is P(A/B) e)what is P(A complement n B) f)Are two events A and B independent? justify your answer. g) Are two events A and B mutually exclusive? Justify your answer.
You are given two identical sets of data A and B with the largest value from...
You are given two identical sets of data A and B with the largest value from the data set B being three times greater than the largest value of data set A. Explain clearly How do the box-and-whisker plots of the two data sets compare?
2) Given sets A, B. Two sets are equivalent if there is a bijection between them....
2) Given sets A, B. Two sets are equivalent if there is a bijection between them. Prove A x B is equivalent to B x A using bijection
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT