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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If A − B = A ∩ B', then (A − B)' is equal to which expression?

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Answer and explanation

Correct answer: A' ∪ B

Use the given identity A − B = A ∩ B'. Taking complements on both sides gives (A − B)' = (A ∩ B')'. Applying De Morgan's law, (X ∩ Y)' = X' ∪ Y', we obtain (A ∩ B')' = A' ∪ (B')' = A' ∪ B. Therefore, option A is correct. The key step is to rewrite set difference before taking the complement.

Tags

setsset-differencecomplementsDe-Morgan-lawsComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A' ∪ B

Why is this the correct answer?

Use the given identity A − B = A ∩ B'. Taking complements on both sides gives (A − B)' = (A ∩ B')'. Applying De Morgan's law, (X ∩ Y)' = X' ∪ Y', we obtain (A ∩ B')' = A' ∪ (B')' = A' ∪ B. Therefore, option A is correct. The key step is to rewrite set difference before taking the complement.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.

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