SETS-5

In a certain school, 180 students take either Chemistry or physics. 130 take chemistry and 100 take both subjects. Find those who take physics only.

Solution

In most cases, OR stands for union whereas AND/BOTH, stands for intersection.

Let Chemistry = n(C), physics = n(P).

n(C)= 130 ,

n(P)= ?

n(CuP) = 180,

n(CnP)= 100

Solution

n(CuP) = n(C) + n(P) - n(CnP)

180  =  130 + n(P)  – 100

180  =  n(P) + 30

180 - 30  =  n(P)

n(P)= 150

physics only = n(P) – n(CnP)

                         = 150 – 100

                         = 50 

Hence those taking only physics are 50.