36 students take the Discrete Structures class. They had 3 quizzes called X, Y , and Z. • Surprisingly, only 1 student did not get an A on any quiz while the rest of the students got an A (aced) on at least one quiz.
• 21 students aced X, 19 students aced Y , and 17 students aced Z. • 9 students aced both X and Y , 11 students aced both X and Z, and 8 students aced both Y and Z.

Required:
a. How many students aced at least one quiz?
b. How many students aced all three quizzes?
c. How may students aced both X and Y but not Z?
d. How may students aced both X and Z but not Y ?
e. How may students aced both Y and Z but not X?