Question

# In a class of 35 students, 17 have Chemistry, 10 have Chemistry but not Physics. If each student of the class has taken either Chemistry or Physics or both, then which of the following is/are true?Number of students taking both Chemistry and Physics is 7.Number of students taking both Chemistry and Physics is 9.Number of students taking Physics but not Chemistry is 18.Number of students taking Physics but not Chemistry is 20.

Solution

## The correct options are A Number of students taking both Chemistry and Physics is 7. C Number of students taking Physics but not Chemistry is 18.Let C denote the set of students who have taken Chemistry and P be the set of students taking Physics. It is given that  n(C∪P)=35, n(C)=17 and n(C−P)=10.Now, n(C−P)=n(C)−n(C∩P)⇒10=17−n(C∩P)⇒n(C∩P)=7Number of students having both Chemistry and Physics are 7.n(C∪P)=n(C)+n(P)−n(C∩P)⇒35=17+n(P)−7⇒n(P)=25n(P−C)=n(P)−n(C∩P)⇒n(P−C)=25−7⇒n(P−C)=18.The number of students taking Physics but not Chemistry is 18.

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