mathslover
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mathslover
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If \(A\cup B = A\cup C\) and \(A \cap B = A \cap C\) . Prove that B = C

shubhamsrg
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dw:1364904134594:dw

shubhamsrg
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dw:1364904215149:dw
dw:1364904255497:dw

shubhamsrg
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both are given to be equal.
which means, except for the common region, other parts should be equal.
dw:1364904349177:dw

shubhamsrg
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now take the case of intersection.
am sure that must help your case ?

mathslover
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Yes! It helped shubham, thanks a lot.

shubhamsrg
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glad to help ^_^

mathslover
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Glad to be helped by you Shubham :)

shubhamsrg
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hehehehe..

shubhamsrg
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glad to be helping you ! ;)

mathslover
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Oh but can I say that as a proof?

shubhamsrg
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sure, venn diagrams are concrete proofs.

shubhamsrg
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well it isnt over yet of course, you got to take the intersection case as well.

mathslover
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Ok! Got it