Final answer:
The problem requires using the principle of inclusion-exclusion to determine how many students like all three subjects. The calculation suggests that 4 students like all three subjects, but this number does not match any of the provided choices, indicating a possible error in the question or answer options.
Step-by-step explanation:
The question asks us to determine how many students like all three subjects: English, Science, and Math. To find this, we use the principle of inclusion-exclusion. First, we add the number of students who like each subject individually: 14 (English) + 19 (Science) + 16 (Math). Next, we subtract the students counted twice because they like two subjects: 13 (English and Science) + 7 (Science and Math) + 5 (Math and English). Finally, we add the number of students who were subtracted twice because they like all three subjects, which is the number we are trying to find.
Calculating the total we get: 14 + 19 + 16 - (13 + 7 + 5) + x = 28
By simplifying, we get: 49 - 25 + x = 28, hence x = 28 - 24 = 4. However, we must consider that the number we calculated, 4, does not fit any of the multiple-choice answers given (a-d). Therefore, there appears to be an error either in the question's values or within the choices given. Without any matching answer option, we cannot conclusively provide one of the choices (a-d) as the correct one.