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m_a_m_a [10]
3 years ago
11

Suppose that S is the set of successful students in a classroom, and that F stands for the set of freshmen students in that clas

sroom.
Find n(S ∩ F) given that n(S) = 54, n(F) = 28 and n(S ∪ F) = 58a) 112b) 24c) 82d) 0e) 140
Mathematics
1 answer:
lora16 [44]3 years ago
3 0

Answer:

b) 24

Step-by-step explanation:

We solve building the Venn's diagram of these sets.

We have that n(S) is the number of succesful students in a classroom.

n(F) is the number of freshmen student in that classroom.

We have that:

n(S) = n(s) + n(S \cap F)

In which n(s) are those who are succeful but not freshmen and n(S \cap F) are those who are succesful and freshmen.

By the same logic, we also have that:

n(F) = n(f) + n(S \cap F)

The union is:

n(S \cup F) = n(s) + n(f) + n(S \cap F)

In which

n(S \cup F) = 58

n(s) = n(S) - n(S \cap F) = 54 - n(S \cap F)

n(f) = n(F) - n(S \cap F) = 28 - n(S \cap F)

So

n(S \cup F) = n(s) + n(f) + n(S \cap F)

58 = 54 - n(S \cap F) + 28 - n(S \cap F) + n(S \cap F)

n(S \cap F) = 24

So the correct answer is:

b) 24

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