Let and be sets

MATHEMATICS · Subjective · CBSE · Mathematics · Sets · Sets

Problem

9. Let

A

and

B

be sets. If

A \cap X=B \cap X=\phi

and

A \cup X=B \cup X

for some set X , show that

\mathrm{A}=\mathrm{B}

. (Hints

\mathrm{A}=\mathrm{A} \cap(\mathrm{A} \cup \mathrm{X}), \mathrm{B}=\mathrm{B} \cap(\mathrm{B} \cup \mathrm{X})

and use Distributive law)