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  1. Merge the two datasets (A and B ) by name excluding Mary. Remember that Mary is not in dataset B
merge(Data_A,Data_B,by.x="name", by.y="name", all.x=F, all.y=T)  # It throws 'Mary'
  1. Merge the two datasets (A and B) keeping all info on both datasets
merge(Data_A,Data_B,by.x="name", by.y="name", all.x=T, all.y=T)  # Keeps all info on both datasets