To Prove: For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U . For all sets A , B and C , if A ⊆ C and B ⊆ C then A ∪ B ⊆ C

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Chapter 6.3, Problem 9ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

39 Two sides of one triangle are congruent to two sides of a second triangle, and the included angles are supplementary. The area of one triangle is 41. Can the area of the second triangle be found?

Answer 2

Question

Chapter 6.3, Problem 9ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

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Answer 3

Question

Chapter 6.3, Problem 9ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

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Answer 4

Question

Chapter 6.3, Problem 9ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

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Answer 5

Chapter 6.3, Problem 9ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

Answer 6

Chapter 6.3, Problem 9ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

Answer 7

Chapter 6.3, Problem 9ES

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

Answer 8

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Answer 9

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Answer 11

Ch. 6.1 - The notation is read”______” and means that___Ch. 6.1 - To use an element argument for proving that a set...Ch. 6.1 - Prob. 3TY Ch. 6.1 - An element x is in AB if , and only if,_______Ch. 6.1 - An element x in AB if, and only if,______Ch. 6.1 - An element x is in B-A if, and only if,______Ch. 6.1 - An elements x is in Acif, and only if.______Ch. 6.1 - The empty set is a set with ______Ch. 6.1 - The power set of a set A is _____Ch. 6.1 - Prob. 10TY

To Prove: For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U . For all sets A , B and C , if A ⊆ C and B ⊆ C then A ∪ B ⊆ C

Solution Summary: The author explains how to prove each statement that is true and find a counterexample for each false statement.

Concept explainers

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

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Chapter 6 Solutions

To Prove: For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U . For all sets A , B and C , if A ⊆ C and B ⊆ C then A ∪ B ⊆ C

Solution Summary: The author explains how to prove each statement that is true and find a counterexample for each false statement.

Concept explainers

To Prove: For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U. For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C

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Chapter 6 Solutions

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,B and C, if A⊆C and B⊆C then A∪B⊆C