We have two sets. One of them is A = {0, 1, 2, 4, 6, 7}. The other is
B = {0, 2, 4, 6, 8}.
2) Being:
n(A U B) = number of elements of the union B
n(A) = number of elements of the set A
n(B) = number of elements of set B
Prove that:
Doing:
A U B = (0, 1, 2, 4, 6, 7, 8} => n (A U B) = 7 (total elements of A union B)
n(A) = 6 (total elements of A)
n(B) = 5 (total elements of B)
So:
Substituting the values in the formula, we have:
7 = 6 + 5 - 4
7 = 7
The formula is correct.
Exercise 2:
In a college, we have 700 students. 400 of them study Chemistry, 310 study Biology and 200 of them
study Biology and Chemistry.
Using set theory, answer the questions below:
A) How many students only study Chemistry (not Biology)?
B) How many students only study Biology (not Chemistry)?
C) How many students study Biology or Chemistry?
D) How many students do not study Biology and Chemistry?
A) If 400 students study chemistry and 200 study Biology and Chemistry, those who only study chemistry are:
B) If 310 students study Biology and 200 study Biology and Chemistry, those who only study Biology are:
C) If 200 students study only Chemistry, 110 only study Biology and 200 study Chemistry and Biology, the
number of students studying Chemistry or Biology is:
200 + 110 + 200 = 510
D) If the college has 700 students and 510 of them study Chemistry or Biology, then the number of students who do not study
neither of the two substances is: n(U) - 510 = 700 - 510 = 190
