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Question

Solve the following problem and verify the data by drawing Venn diagrams. In a class, 50 students offered Mathematics, 42 offered Biology and 24 offered both the subjects. Find the number of students, who offer Biology only.

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Solution

Let the total number of students who offered mathematics be n(M) and number of students who offered biology be n(B).

Then, the number of students who offered both mathematics and biology is n(MB) and the number of students who offer biology only is n(B)n(MB)

We know that n(AB)=n(A)+n(B)n(AB) where A and B are the respective sets.

Here, it is given that in a class, 50 students offered mathematics, 42 offered biology and 24 offered both the subjects, that is n(M)=50,n(B)=42 and n(MB)=24 and therefore,

n(B)n(MB)=4224=18

Hence, the number of students who offer biology only is 18.

628012_562498_ans_f30fe4fd581f45afa7de0fd886935802.png

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