Question

Let A and B be sets. Consider the following statement: A ∪ (B − A) ⊆...

Let A and B be sets. Consider the following statement: A ∪ (B − A) ⊆ A ∪ B

a) Draw and label a Venn diagram to illustrate this statement.

b) Prove this statement.

please clearly show illustration and work

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(10) Consider the following property: For all sets A, B and C, (A-B)∩(A-C)=A-(B∪C) a. Construct a...
(10) Consider the following property: For all sets A, B and C, (A-B)∩(A-C)=A-(B∪C) a. Construct a proof of this property using set definitions. b. Prove this property using a set-membership table, clearly stating how the table proves the property. c. Illustrate this property using Venn diagrams, clearly stating how the diagram proves the property. You must use a separate Venn diagram for the set on the left hand side of the equal sign, and for the set on the right...
Set Operations In questions 7 and 8 Let A = {0, 2, 4, 6}, B =...
Set Operations In questions 7 and 8 Let A = {0, 2, 4, 6}, B = {0, 1, 2, 3}, and C = {4, 5, 6}. U = {x∈ℤ| 0≤x≤10} 7. Find (A ∪ B) – C’. 8. Find C ∩ (A’ ⊕ B’) Venn Diagrams Draw Venn diagrams for the following set operations. Show each step and label the sets as well as what the diagram is showing Ex: if the Venn diagram is showing C’, label the rectangle...
Problem 3.9. Let A and B be sets. Prove that A × ∅ = ∅ ×...
Problem 3.9. Let A and B be sets. Prove that A × ∅ = ∅ × B = ∅. Please write your answer as clearly as possible, appreciate it!
Definition 1. The symmetric difference of two sets A and B is the set A△B defined...
Definition 1. The symmetric difference of two sets A and B is the set A△B defined by A△B = (A \ B) ∪ (B \ A). (a) Draw the Venn diagram for the symmetric difference. (b) Prove that A△B = (A ∪ B) \ (A ∩ B). (c) Prove A△A = ∅, A△∅ = A. (d) Prove that for sets A, B, we have A△B = A \ B if and only if B ⊆ A.
. Do the following problems: a. Find the sets A and B, if A – B...
. Do the following problems: a. Find the sets A and B, if A – B = {1, 5, 7, 8}, B – A = {2, 10} and A ꓵ B = {3, 6, 9}. b. Draw a Venn Diagram for the Symmetric Difference of the sets A and B. c. Find and list all the partitions of S = {a, b, c, d, e}.
Using any method, show that for all sets A and B which are subsets of a...
Using any method, show that for all sets A and B which are subsets of a universe U, that A − (A − B) = A ∩ B. Note. No proofs by Venn diagram will be accepted.** Algebraic Prove should be good.
(a) Suppose A, B and D are sets with the following properties: A ∩ B =...
(a) Suppose A, B and D are sets with the following properties: A ∩ B = A,     B ∩ D = D        ,   ( Ac ∪ Dc)c = ∅     Draw a venn diagram for these sets and hence shade the region                                                       ( Ac \ Bc) ∩ Dc     (b)   Given that P(A U B) = k, P( A ) = 0.4, P( B ) = 0.2, determine the value of k if       (i)    A and B are independent....
(a) Suppose A, B and D are sets with the following properties: A ∩ B =...
(a) Suppose A, B and D are sets with the following properties: A ∩ B = A,     B ∩ D = D        ,   ( Ac ∪ Dc)c = ∅     Draw a venn diagram for these sets and hence shade the region                                                       ( Ac \ Bc) ∩ Dc     (b)   Given that P(A U B) = k, P( A ) = 0.4, P( B ) = 0.2, determine the value of k if       (i)    A and B are independent....
Let A,B and C be sets, show(Prove) that (A-B)-C = (A-C)-(B-C).
Let A,B and C be sets, show(Prove) that (A-B)-C = (A-C)-(B-C).
3. Prove or disprove the following statement: If A and B are finite sets, then |A...
3. Prove or disprove the following statement: If A and B are finite sets, then |A ∪ B| = |A| + |B|.