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Prove that (A-B) intersect(C-B)=(A intersect C)-B

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Prove that (A-B) intersect(C-B)=(A intersect C)-B

Posted by Faiz Khan 6 years, 7 months ago

CBSE > Class 11 > Mathematics

1 answers

Keshav Bindal 6 years, 7 months ago

(i) let x belongs to (A-B) intersection (C-B) => x E (A-B) and x E (C-B) => [x E A and x not E B] and [x E C and x not E B] => [x E A and x E C]and x not E B => x E (A intersection C) and x not E B => x E (A intersection C)-B. Therefore, (A-B) intersection (C-B) is subset of (A intersection C)-B. (ii) [Repeat (i) from last to starting] Therefore, (A intersection C)-B is subset of (A-B) intersection (C-B). Hence, from (i) and (ii) (A-B) intersection (C-B) = (A intersection C)-B

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