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A,B,C are three sets such that AUB=AUC and AnB=AnC: A)B=C B)A=B=C C)A=2B D)A=Phi

A,B,C are three sets such that AUB=AUC and AnB=AnC:
A)B=C
B)A=B=C
C)A=2B
D)A=Phi

Grade:10

1 Answers

Arun
25763 Points
10 months ago
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.  

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