Let `A`, `B` and `C` be the sets such that `A uu B=A uu C` and `A nn B = A nn C`. Show that `B=C`
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
(i) `because` Sets A, B and C are such that
`A cup B = A cup C`
or `(A cup B) cap B = (A cupC) cap B`
or `(A cap B) cup (B cap B) = (A cap B) cup (C cap B)` (From distributive law)
or `B = (A cap B) cup (C cap B)` ….(1)
[Since `(A cap B) cup (B cap B)=B`]
Again `(A cup B) = (A cup C)`
or `(A cup B) cap C = (A cup C) cap C`
or `(A cap C) cup (B cap C)= (A cap C) cup (C cap C)` [From distributive law)
or `(A cap C) cup (B cap C) = C` [Since `(A cap B) cup (C cap C)=C`]
then `C = (A cap C) cup (B cup C)`…(2)
`because` Given `A cap B = A capC` then, replace `(A cap C)` by `(A cap B)` in equation (2),
`C = (A cap B) cup (B cup C)`…(3)
Now comparing equation (1) and equation (3),
`B=C`.