SOLUTION: A survey of 51 pet owners revealed that 32 owned dogs, 38 owned cats, and 3 owned neither cats nor dogs. How many owned cats and dogs?

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Question 353273: A survey of 51 pet owners revealed that 32 owned dogs, 38 owned cats, and 3 owned neither cats nor dogs. How many owned cats and dogs?
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
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No. of owners having any one of these pet = 51 - 3 = 48
thus n(A U B) = 48 , no. of owners having any pet

n(A) = 32 , no. of owner having dogs
n(B) = 38 , no. of owner having cats

now we have to find no. of owners having cats and dogs n (A∩B)
as we know n (A∩B) = n(A ) + n (B) - n(A U B)


= n(A ) + n (B) - n(A U B)
= 32 + 38 - 48
= 22