Question

Let A, B, and C be the sets such that AUB=AU C and A n B=A n C. Show
that B=C.
​

Answer 1

Step-by-step explanation:

Given that AUB = AUC

⇒ (AUB) ∩ C = (AUC) ∩C

⇒ (A∩C) U (B∩C) = C [ ∴(AUC)∩C = C ]

⇒ (A∩B) U (B∩C) = C ..........(1) [ ∴(A∩C) = A∩B ]

Again AUB = AUC

(AUB) ∩ B = (AUC) ∩ B

B = (A∩B) U (C∩B)

= (A∩B) U (B∩C) ...........(2)

From 1 & 2 we get

B = C

Answer 2

Answer:

Please check it

Please check it Mark it Brainlist

Please check it Mark it Brainlist FOLLOW ME

Please check it Mark it Brainlist FOLLOW ME THANK YOU