The given information can be analysed as follows :
Let 'O' denote optional and 'C' denote compulsory .
| |
A |
B |
C |
D |
E |
F |
| History |
C |
C |
C |
O |
- |
- |
| Physics |
- |
- |
- |
- |
C |
O |
| Mathematics |
- |
- |
O |
- |
O |
C |
| English |
O |
- |
- |
C |
- |
- |
| Chemistry |
- |
O |
- |
- |
- |
- |
One compulsory subject of F is Mathematic. F has Physics as one of the subjects. So, Physics is optional of F. F has Mathematics as optional and Physics as one subject.
So, Physics is the compulsory subject of E. A and D have the same subjects -- History and English. D has History as optional subject and so English is the compulsory subject of D. Subjects of A and D are reverse in regard of optional and compulsory.
So, A has History as compulsory subject and English as optional.
Chemistry is the optional subject of only one teacher. So, it is the optional of B, which only remains.
We know that History is the compulsory subject of three teachers. So, it is compulsory for A, B and C.
D is the teacher having English as her compulsory subject.
So, D is the only female teacher.
C's compulsory subject is History.