Question

Let A,B and C be the sets such that A U B =A U C and A intersection B =A intersection C show that B=C.
pls reply as soon as possible
also explain

Answer 1

B = C If $\bold{A\cup B = A\cup C}$ and $\bold{A\cap B=A\cap C}$ and A , B and C be the sets.  

Given:

A, B and C be the sets such that $A\cup B=A\cup C$

$A\cap B=A\cap C$

To show:

B = C  

Proof:

As we can see in the question that the value of X in the scenario of A∪B=A∪C, now as we can see that all the value of B is in A and C, therefore X is equal to both A and X

$X\in A,X \in B$

Now the question says that A∩B=A∩C

Thus we can say that both C and B have the value of A in their sets respectively, therefore, we can also say that if values of B are in C, then vice versa is also possible.

$X \in A, X \in C$

Therefore, taking both the cases we can say that the values of B are in C and vice versa,

Hence, B = C.  

Hence Proved.

Answer 2

Answer:

this is the answer I think you will understand it ok