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If A ⊂ B, then A̅ ∩ B̅ = ?

If A ⊂ B, then A̅ ∩ B̅ = ? Correct Answer B̅

Concept:

Set Theory:

De Morgan's Law:

  • (A ∪ B)' = A' ∩ B'.
  • (A ∩ B)' = A' ∪ B'.


Calculation:

Using the De Morgan's law, we get:

A̅ ∩ B̅ = (A ∪ B)'

Since A ⊂ B, therefore A ∪ B = B.

⇒ A̅ ∩ B̅ = (A ∪ B)' = B' which is also written as B̅.

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