1.

In a certain group of 36 people only 18 are wearing hats and only 24 are wearing sweaters .if six people are wearing neither a hat nor a sweater ,then how many people are wearing both a hat a sweater?​

Answer»

N(U)=36

n(HATS)=18=n(H)

n(SWEATERS)=24=n(S)

n(Wearing neither hat nor Sweater) =6

n(S∪H)=n(U)− n(Wearing neither hat nor sweater) =36−6=30

n(S∪H)=n(S)+n(H)−n(S∩H)

30=24+18−n(S∩H)

n(S∩H)=42−30=12

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