point the step in the argument that is not valid and explain why ? Theorum: For all sets A,B   A’∪B’ ⊆ (A ∪B)’ . Proof: Suppose A and B are sets , and x ∈ A’ ∪ B’. Then x ∈ A’ or x  ∈ B’ by the defination of union . It follows that x∉A or x∉B by the defination of complement . , and so x∉ A ∪ B by the defination of union .Thus , x ∈ (A ∪ B)’

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A: Please see the answer below.

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A:

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A:

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A:

Q: 1.2 Now consider the following sets: X {(x, y) : x² + y² < 4} (5) %3D Y = {(x, y) : -x +y < -2} (6)…

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A:

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A:

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A:

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A: The solution is as shown below

Q: Đ A is a closed set.

A:

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A: ANSWER :

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A: we know thatA∪B=x: x∈A or x∈BA∩B=x: x∈A or x∈BA'=x:x∈U, x∉A=U \ AWhere U is a universal set.That is…

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A: We will  prove the given statement using mathematical induction method.

Q: n so is {A} but do NOT use an the argu

A: To prove that if A is a set then so is A.

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A:

Q: uppose that ℱ is a non-empty family of sets, B is a set, and ∀A ∈ ℱ (A ⊆ B). Is ∪ℱ ⊆ B? Either…

A: Given: To explain the given statement as follows,

Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

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A:

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A:

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Q: 1. Decide whether the folloring stabe ments ae false . Justify true or (a) YxeTR, ¥yeR, x²-y² z xy…

A: 1. a ∀ x ∈  R, ∀ x ∈  R, x2+y2 ≥ 2xy  TRUE. Because,  ∀ x ∈  R, and ∀ x ∈  R we have (x-y)2 ≥ 0.…

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A:

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A:

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A: 3 Given A is any set. We have to prove that A is also a set. Since, A is any set Then as every set…

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A:

Q: Consider the following statement. For all sets A and B, AC U BC C (AU B)C. The following is a…

A: The solution are next step

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A:

Q: Fill in the boxes in the following proof by contradiction that: For all sets A and B, if B ⊆ A'…

A: For all sets A and B, if B ⊆ A' then A ∩ B = Ø

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A: Here below the sentences written as proper order.

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Q: 2. Prove that by laws of set, (A - B)- (B - C) = A -B

A:

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A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…