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prove that if A U B=C and A INTERSECTION B={ } THEN A=C-B

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Manisha asked in Math

prove that if A U B=C and A INTERSECTION B={ } THEN A=C-B

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Varun Rawat answered this
18265 helpful votes in Math, Class XII-Science

Here is the link given below for the answer to your query.

Please follow the solution of part (3) in the given link :

https://www.meritnation.com/discuss/question/5412692/1/

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123456789 answered this
959 helpful votes in Math, Class XII-Science

Given:-

AUB = C

AnB = { }

.

Using first given equation:-

AUB = C

Intersecting both sides by B' (B compliment)

.

(AUB) n B' = C n B'

removing the bracket:-

(AnB') U (BnB') = C n B'

.

Here by the second given equation:-

AnB = { }

This means,

AnB' = A .... (A and B are disjoint sets)

.

= (AnB') U (BnB') = C n B'

And Here:- AnB' = A ; BnB' = { } ; and CnB' = C-B

.

= A U { } = C - B

= A = C-B

Hence proved.