If A and B are two non empty sets then A union B=B intersection iff
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Step-by-step explanation:
Let M = (A ∩ B)' and N = A' U B'
Let x be an arbitrary element of M then x ∈ M ⇒ x ∈ (A ∩ B)'
⇒ x ∉ (A ∩ B)
⇒ x ∉ A or x ∉ B
⇒ x ∈ A' or x ∈ B'
⇒ x ∈ A' U B'
⇒ x ∈ N
Therefore, M ⊂ N …………….. (i)
Again, let y be an arbitrary element of N then y ∈ N ⇒ y ∈ A' U B'
⇒ y ∈ A' or y ∈ B'
⇒ y ∉ A or y ∉ B
⇒ y ∉ (A ∩ B)
⇒ y ∈ (A ∩ B)'
⇒ y ∈ M
Therefore, N ⊂ M …………….. (ii)
Now combine (i) and (ii) we get; M = N i.e. (A ∩ B)' = A' U B'
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Answer:
A=B
Step-by-step explanation:
A=B
this is correct answer
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