Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

Question

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

Filo · Accepted Answer

At maximum there are 170 students majoring in at least one of the sciences and a minimum of 150 majoring in at least one of the sciences.

n (A \cap B) = n (A) + n (B) - n (A \cup B)

= 150 + 130 - 170 = 110

This is minimum no. of people majoring in both chemistry and biology.

= 150 + 130 - 150 = 130

This is maximum no. of people majoring in both chemistry and biology.

Question Text	Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from
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