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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesHardLevel 20

If A △ B = (A ∩ B′) ∪ (A′ ∩ B), what is (A △ B)′ equal to?

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Answer and explanation

Correct answer: (A ∩ B) ∪ (A′ ∩ B′)

The symmetric difference A △ B consists of elements belonging to exactly one of A and B. Its complement therefore consists of elements that belong to both sets or to neither set. The ‘both’ part is A ∩ B, and the ‘neither’ part is A′ ∩ B′. Taking their union gives (A △ B)′ = (A ∩ B) ∪ (A′ ∩ B′).

Tags

setscomplementsymmetric-differenceBoolean-identityComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

(A ∩ B) ∪ (A′ ∩ B′)

Why is this the correct answer?

The symmetric difference A △ B consists of elements belonging to exactly one of A and B. Its complement therefore consists of elements that belong to both sets or to neither set. The ‘both’ part is A ∩ B, and the ‘neither’ part is A′ ∩ B′. Taking their union gives (A △ B)′ = (A ∩ B) ∪ (A′ ∩ B′).

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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