Question

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?
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Answer 1

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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Answer 2

Answer:

36-6= 30 (people who are wearing either or both.)

Now out of 30 people 18 are wearing hats and 24 are wearing sweaters.

30-24=6 and 30-18=12

so 6 people are not wearing sweaters and 12 people are not wearing hats from the 30 people.

so  6+12= 20 people are wearing only one of the twp things.

therefore, 10 people are wearing both.