phamthithutrang1008 phamthithutrang1008

06-10-2021
Mathematics

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Let A, B, C, X be sets with A, B, and C are subsets of X. Prove the following set equalities
a) (A ∩ B)' = A' ∪ B'

Respuesta :

discipulus discipulus

06-10-2021

Answer:

[tex] let \:x \in (A\cap B)'\\\Rightarrow x \notin (A\cap B) \\\Rightarrow x \notin A \:or\: x\notin B\\ \Rightarrow x \in A' \:or \:x \in B'\\\Rightarrow x \in A' \cup B'\\\therefore (A ∩ B)' = A' ∪ B' [/tex]

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