In a class of 45 students, 32 offered physics (P), 28 offered government (G), and 12 did not offer any of the two subjects.
i. Draw a venn diagram to represent information.
ii. what is PuG
i.
```
P (Physics)
/ \
/ \
/ \
G (Government) Neither
```
ii. PuG represents the intersection of the two sets, or the number of students who offered both physics and government. To find PuG, we add the number of students who offered physics (32) to the number of students who offered government (28), and then subtract the total number of students in the class (45) to account for double counting:
PuG = 32 + 28 - 45
PuG = 60 - 45
PuG = 15
Therefore, 15 students offered both physics and government.