Question

1, In a class of 80 students in Debreberhan University, 45 are good in mathematics, 15 are good in both mathematics and in English, 13 are good in both mathematics and psychology, 16 are good in both English and psychology only, 20 are good in psychology and 9 are good in both of the three courses.
a) How many students are good in mathematics only? b) How many students are not good in any of the three course?​

Answer 1

Treating the data as a Venn set, it is found that:

• 26 students are good in mathematics only.

• 28 students are not good in any of the three courses.

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I am going to say that:

• A is the number of students good in Math.
• B is the number of students good in English.
• C is the number of students good in Psychology.

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9 are good in all of the three courses.

This means that: $A \cap B \cap C = 9$

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13 are good in both mathematics and psychology

This means that:

$(A \cap C) + (A \cap B \cap C) = 13$

$(A \cap C) + 9 = 13$

$(A \cap C) = 4$

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15 are good in both mathematics and in English

This means that:

$(A \cap B) + (A \cap B \cap C) = 15$

$(A \cap B) + 9 = 15$

$(A \cap B) = 6$

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16 are good in both English and psychology

This means that:

$(B \cap C) + (A \cap B \cap C) = 16$

$(B \cap C) + 9 = 16$

$(B \cap C) = 7$

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20 are good in psychology

This means that:

$c + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 20$

$c + 4 + 7 + 9 = 20$

$c = 0$

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45 are good in mathematics

This means that:

$a + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 45$

$a + 6 + 4 + 9 = 45$

$a = 26$

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Question a:

$a = 26$, which means that 26 students are good in mathematics only.

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Question b:

At least one is:

$a + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 26 + 6 + 4 + 7 + 9 = 52$

Thus, 80 - 52 = 28

28 students are not good in any of the three courses.

A similar problem is given at: brainly.com/question/22003843