The number of students in this group who are enrolled in MATH 101 or ENG 101

Question

Suppose in a group of 23 students 15 are enrolled in MATH 101, and 12 are enrolled in ENG 101. If there are 5 students in this group who are not enrolled in any of these two classes, find

a) The number of students in this group who are enrolled in MATH 101 or ENG 101: Answer = ________

b) The number of students in this group who are enrolled in both MATH 101 and ENG 101: Answer = _______

c) The number of students in this group who are enrolled in exactly one of the two classes: Answer =

Answer 1

Let $M = \{students\ enrolled\ in\ MTH101\}$ and $E = \{students\ enrolled \ in \ ENG101\}$

a) total - not enrolled in any course i.e $23-5 =18$

b) $M\cup E = M + E - M\cap E$ so , 18 = 15 + 12 - $M\cap E$

  you need 

$ M\cap E $

c) it's just $M - M\cap E$

and $E - E\cap M$