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please help me with this: Are the following true or false, if they are false show with an example - Let A, B and C

please help me with this: Are the following true or false, if they are false show with an example

- Let A, B and C be events withP(ABC)=1 and P(BC)>0. ThenP(AcBC)>0

- Let D and E be events with P(D)>0. ThenP(DEcDE)P(EcD)

-Let S and T be two independent events with 0<P(S)<1and 0<P(T)<1. Define the events Y=STandZ=TS. Then Y and Z are independent

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