how does natural selection influence the effectiveness of antibiotics and the virulence of infectious agents

Most bacteria will die at first when an antibiotic is administered. But few bacterial cells will live. Those cells that live will reproduce and give that trait that is resistant against the antibiotic to their "kids." Therefore, the next generation of bacteria will be resistant to the antibiotic and the antibiotic will not be able to kill the bacteria infection. So in this case, natural selection was able to kill off the bacteria that wasn't resistant to the antibiotic and only the "fittest" survived