If A, B and C be sets. Then, show that `A nn (B uu C) = (A nn B) uu (A – InterviewSolution

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1.	If A, B and C be sets. Then, show that `A nn (B uu C) = (A nn B) uu (A nn C)`.
Answer» Let `x in A nn (B uu C)` `rArr x in A` and `x in (B uu C)` `rArr x in A` and (`x in B` or `x in C`) `rArr` (`x in A` and `x in B`) or `(x in A "and" x in C)` `rArr x in A nn B` or `x in A nn C` `x in (A nn B) uu (A nn C)` `rArr A nn (B uu C) sub (A nn B) uu (A nn C)` `rArr A nn (B uu C) sub (A nn B) uu (A nn C)` Again, let `y in (A nn B) uu (A nn C) "......"(i)` `rArr y in (A nn B)` or `y in (A nn C)` `rArr (y in A "and" y in B)` or `(y in A "and" y in C)` `rArr y in A` and `(y in B "or" y in C)` `rArr y in A` and ` y in B uu C` `rArr y in A nn (B uu C)` `rArr (A nn B) uu (A nn C) sub A nn (B uu C)"......."(ii)` From Eqs. (i) and (ii). `A nn (B uu C) = (A nn B) uu (A nn C)`

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