Question

In a class of 100 students 90 have taken mathematics 70 have taken mathematics but not biology. Find the number of students who have taken biology but not mathematics. Each student has taken either mathematics or biology or both. *
30
10
15
20​

Answer 1

Answer:

10

Step-by-step explanation:

90-70= 20 is the number of students who took biology and Mathematics.

n(M U B)=100

100-70-20=10

Answer 2

SOLUTION

GIVEN

In a class of 100 students 90 have taken mathematics 70 have taken mathematics but not biology. Each student has taken either mathematics or biology or both.

TO CHOOSE THE CORRECT OPTION

The number of students who have taken biology but not mathematics.

• 30

• 10

• 15

• 20

EVALUATION

Let

M = Students who have taken Mathematics

B = Students who have taken Biology

Then by the given condition

$\sf{n(M \cup B)} = 100$

$\sf{n(M)} = 90$

$\sf{n(M \cap B' \: )} = 70$

Now

$\sf{n(M \cap B' \: )} = 70 \: \: gives$

$\sf{n(M) - n(M \cap B \: )} = 70$

$\implies \sf{90 - n(M \cap B \: )} = 70$

$\implies \sf{ n(M \cap B \: )} = 20$

Again

$\sf{n(M \cup B)} = 100 \: \: \: gives$

$\sf{n(M) + n( B) - n(M \cap B)= 100\: }$

$\implies \sf{90+ n( B) - 20= 100\: }$

$\implies \sf{ n( B) = 30\: }$

Hence the number of students who have taken biology but not mathematics

$= \sf{n(B \cap \: M ' \: )}$

$= \sf{n(B ) - n(B \cap M )\: )}$

$= \sf{30 - 20\: }$

$= \sf{10}$

FINAL ANSWER

The number of students who have taken biology but not mathematics is 10

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