Herd immunity is achieved when a sufficient portion of a population is immune to an infectious disease, either through vaccination or previous infections, reducing the likelihood of infection for individuals who are not immune.
In the examples provided, the first option states that "40% of the population has been vaccinated; 50% of the population has been exposed to the pathogen." This means that a total of 90% (40% vaccinated + 50% exposed) of the population has some level of immunity to the pathogen, which is likely to be sufficient to reach herd immunity, depending on the specific disease.
Therefore, this example would be considered to have reached herd immunity.