In a locality there are 125 people living in an apartment out of them (4^1/2+27^1/3) are alcoholic find the number of people who drink. what value is depicted here
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Given:
In hostel
Total number of students =125
Number of students who drink tea=80
Number of students who drink coffee=60
Number of students who drink tea and coffee=20
To find:
Number of students who do not drink tea or coffee.
Solution:
Let
A=Tea
B=Coffee
n(A)=80
n(B)=60
U=125
n(A\cap B)=20n(A∩B)=20
We know that
n(A\cup B)=n(A)+n(B)-n(A\cap B)n(A∪B)=n(A)+n(B)−n(A∩B)
Using the formula
n(A\cup B)=80+60-20=120n(A∪B)=80+60−20=120
n(A\cup B)'=U-n(A\cup B)=125-120=5n(A∪B)
′
=U−n(A∪B)=125−120=5
Hence, the number of students who do not drink tea or coffee=5
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