- #1
MathematicalPhysicist
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Problem Statement:
Let Y be a subset of X, and X and Y are connected, show that if A and B form a separation of X-Y then YUA and YUB are connected.
Attempt at solution:
Well I'm not sure where the fact that X is connected comes to play (perhaps it gurantees us the possibility of X-Y not to be connected).
anyway if we look at: seperations of YUB=CUD and YUA=C'UD'
then Y=(YUB)-B=(C-B)U(D-B), Y=(YUA)-A=(C'-A)U(D'-A)
which are both seperations of Y which is a contradiction to Y being connected, am I correct here or yet again wrong?
any input?
thanks in advance.
Let Y be a subset of X, and X and Y are connected, show that if A and B form a separation of X-Y then YUA and YUB are connected.
Attempt at solution:
Well I'm not sure where the fact that X is connected comes to play (perhaps it gurantees us the possibility of X-Y not to be connected).
anyway if we look at: seperations of YUB=CUD and YUA=C'UD'
then Y=(YUB)-B=(C-B)U(D-B), Y=(YUA)-A=(C'-A)U(D'-A)
which are both seperations of Y which is a contradiction to Y being connected, am I correct here or yet again wrong?
any input?
thanks in advance.