Sampling f fraction out of n records:
Last two can be seen by considering an adversarial case. Under the binomial distribution, there is a non-zero probability of sampling the entire population. Since any sampled subset can never recreate the entire population, S with R and S without R can never be converted to the coin flips semantics.
Source: S. Chaudhuri, R. Motwani, V. Narasayya; On random Sampling over Joins.