Question

his is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

Prove De Morgan's law by showing that A∪ B¯¯¯¯¯¯¯¯¯A⁢∪ B¯ = A¯¯¯A¯ ∩ B¯¯¯∩ B¯ if A and B are sets.

Prove De Morgan's law by showing that each side is a subset of the other side by considering x ∈ A¯¯¯A¯ ∩ B¯¯¯B¯ .

Rank the options below.

• Therefore, we get x ∈    A¯¯¯∩B¯¯¯A¯∩B¯ → A∪B¯¯¯¯¯¯¯¯¯A∪B¯ .

  Therefore, we get x ∈     A¯∩B¯ → A∪B¯ . Open choices for matching

  No answer1234567

• Applying De Morgan's law of proposition, we get ¬(x ∈ A ∨ x ∈ B).

  Applying De Morgan's law of proposition, we get ¬(x ∈ A ∨ x ∈ B). Open choices for matching

  No answer1234567

• Then, we can write ¬(x ∈ A) ∧ ¬(x ∈ B).

  Then, we can write ¬(x ∈ A) ∧ ¬(x ∈ B). Open choices for matching

  No answer1234567

• Consider x ∈ A¯¯¯∩B¯¯¯A¯∩B¯ .

  Consider x ∈ A¯¯¯∩B¯¯¯A¯∩B¯<math id="formula597.mml" xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>A</mi><mo>¯</mo></mover><mo>∩</mo><mover><mi>B</mi><mo>¯</mo></mover></math> . Open choices for matching2

  No answer1234567

• Using the definition of intersection, x ∈ A¯¯¯A¯ ∧ x ∈ B¯¯¯B¯ .

  Using the definition of intersection, x ∈ A¯ ∧ x ∈ B¯ . Open choices for matching

  No answer1234567

• Using the definition of the complement of a set, x ∉ A ∧ x ∉ B.

  Using the definition of the complement of a set, x ∉ A ∧ x ∉ B. Open choices for matching

  No answer1234567

• Hence, A∪B¯¯¯¯¯¯¯¯¯A∪B¯ is true.

  Hence, A∪B¯¯¯¯¯¯¯¯¯A∪B¯< what is the order

Answer 1

question wasn't clear . But this solution might be useful.