Question

Question 11 Let A and B be sets. If A∩X = B∩X = Φ and A∪X = B∪X for some set X, show that A = B.

(Hints A = A∩(A∪X), B = B∩(B∪X) and use distributive law)

Class XI - Sets Page 27

Answer 1

SOLUTION

TO PROVE

Let A and B be sets. If A∩X = B∩X = Φ and A∪X = B∪X for some set X, show that A = B.

EVALUATION

Here it is given that

A and B be sets.

A∩X = B∩X = Φ and A∪X = B∪X for some set X

Now

A

= A ∩ ( A U X ) [ Absorptive law ]

= A ∩ ( B U X ) ( ∵ A ∪ X = B ∪ X )

= ( A ∩ B ) U ( A ∩ X ) [ Distributive law]

= ( A ∩ B ) U Φ ( ∵ A ∩ X = Φ )

= ( A ∩ B )

= B ∩ A

= ( B ∩ A ) U Φ

= ( B ∩ A ) U ( B ∩ X )

= B ∩ ( A U X ) [ Distributive law]

= B ∩ ( B U X ) ( ∵ A ∪ X = B ∪ X )

= B [ Absorptive law ]

Hence proved

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Answer 2

Step-by-step explanation:

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