If nB 16 n A union B 22 and nA interset B 6 find nA In a

If n(B) = 16, n (A union B) = 22, and n(A interset B) = 6, find n(A). In a survey of 215 people, a pet food manufacturer found that 53 owned a dog but not a cat, 23 owned a cat but not a dog, and 82 owned neither a dog or a cat. How many owned both a cat and a dog? How many owned a dog? Let A and 8 be subsets of a universal set union and suppose n[union) = 48, n(A) = 12, n(B) = 22, and n(An 8) = 7. Compute: n(A^C interset B) = n(B^C) = n(A^C interset B^C) = How many subsets does A have? How many proper subsets does A have?

Solution

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n(B) = 16

n(AUB) = 22

n(AnB) = 6

Lets find n(A) using the formula

n(AUB) = n(A) + n(B)- n(AnB)

substitute the values

22 = n(A) + 16 - 6

22 =n(A) +10

22-10= n(A)

12=n(A)

Answer:

n(A) = 12