In an office 37 people prefer x drink, 32 people prefer y drink and 41 people refer z drink - Maths - Sets Relations and Functions

Question

In an office 37 people prefer x drink, 32 people prefer y drink and
41 people refer z drink Also, 5 employees prefer all the types of
drinks and 15 people prefer
atleast two types of drinks If each of the employees prefer at
least one type of drink , then how many employees are there in the
office?

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

According to question:nX=37nY=32nZ=41nX∩Y∩Z=5According to question, 15 people prefer atleast two types of drinks
 Atleast two means two or more than two,⇒nX∩Y+nY∩Z+nZ∩X-2nX∩Y∩Z=15⇒nX∩Y+nY∩Z+nZ∩X-10=15⇒nX∩Y+nY∩Z+nZ∩X=25We know thatnX∪Y∪Z=nX+nY+nZ-nX∩Y+nY∩Z+nZ∩X+nX∩Y∩Z=37+32+41-25+5nX∪Y∪Z=90Hence there are 90 employees in the office

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