- #1
INdeWATERS
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I am having issues with a proof, as follows.
*U = universal set , P(U) = power set of a universal set
For all sets A, B, C ∈ P(U), if A ⊆ C and B ⊆ C, then A ⊆ B or B ⊆ A.
I am pretty sure the statement is false and so I have to disprove it, i.e. prove the negation. I am stuck on how to negate. My attempts are as follows...
(1) There exist sets A, B, C ∈ P(U) such that A ⊆ C or B ⊆ C and A ⊄ B and B ⊄ A.
(2) There exist sets A, B, C ∈ P(U) such that if A ⊆ C or B ⊆ C then A ⊄ B and B ⊄ A.
Would the contrapositive of the statement be easier to work with??
For all sets A, B, C ∈ P(U), if A ⊆ B or B ⊆ A then, A ⊆ C and B ⊆ C.
Thank you for your time and help!
*U = universal set , P(U) = power set of a universal set
For all sets A, B, C ∈ P(U), if A ⊆ C and B ⊆ C, then A ⊆ B or B ⊆ A.
I am pretty sure the statement is false and so I have to disprove it, i.e. prove the negation. I am stuck on how to negate. My attempts are as follows...
(1) There exist sets A, B, C ∈ P(U) such that A ⊆ C or B ⊆ C and A ⊄ B and B ⊄ A.
(2) There exist sets A, B, C ∈ P(U) such that if A ⊆ C or B ⊆ C then A ⊄ B and B ⊄ A.
Would the contrapositive of the statement be easier to work with??
For all sets A, B, C ∈ P(U), if A ⊆ B or B ⊆ A then, A ⊆ C and B ⊆ C.
Thank you for your time and help!
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