In a class of 100 students, 60 like mathematics, 72 like physics, 68 like chemistry and no student likes all three subjects. Then number of students who don't like mathematics and chemistry is
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Solution
Let M, P and C represents the set of students who likes Mathematics, Physics and Chemistry respectively as shown in venn diagram below:
From the venn diagram, we have n(M∩P)=x,n(M∩C)=yandn(P∩C)=z
As we know, n(M∪P∪C)=n(M)+n(P)+n(C)−n(M∩P)−n(M∩C)−n(P∩C)+n(M∩P∩C) ⇒100=60+72+68−(x+y+z)+0x+y+z=100
Since, no student like only maths, or only physics or only chemistry
So x+y=60x+z=72y+z=68⎫⎪⎬⎪⎭⇒y=28
Now the number of students who don't like mathematics and chemistry is given by n(M′∩C′)=100−n(M∪C) =100−(60+68−y)=y−28=0