Question

If A, B, C are three sets such that AUB= AUC and AintersectB = AintersectC then
(a) A = B (b) B = C (c) A =C
(d) A=B=C

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Answer 1

Answer:

B = C If and and A , B and C be the sets.  

Given:

A, B and C be the sets such that

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

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.

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

Hence, B = C.  

sᴏ ᴏᴘᴛɪᴏɴ b. is the right answer

Answer 2

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