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Mathematics, 13.03.2020 02:10 vrw28

Suppose a list A contains the 30 students in a mathematics class, and a list B contains the 35 students in an English class, and suppose there are 20 names on both lists. Find the number of students: (a) only on list A, (b) only on list B, (c) on list A or B (or both), (d) on exactly one list.

a. List A has 30 names and 20 are on list B; hence 30 - 20 =10 names are only on list A.
b. Similarly, 35 -20 =15 are only on list B.
c. We seek n(A U B). By inclusion—exclusion,
n(AU B) = n(A) +n(B)- n(A⋂ B) = 30+35 -20 —45.
In other words, we combine the two lists and then cross out the 20 names which appear twice.
d. By (a) and (b), 10 + 15= 25 names are only on one list; that is, n(A⊕ B)= 25.

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