Slide 1 : EXAMPLE 4
Slide 2 : EXAMPLE 4 There are 260 persons with a skin disorder.
Slide 3 : EXAMPLE 4 There are 260 persons with a skin disorder. If 150 had been exposed
to the chemical A,
Slide 4 : EXAMPLE 4 There are 260 persons with a skin disorder. If 150 had been exposed
to the chemical A, 74 to the chemical B and
Slide 5 : EXAMPLE 4 There are 260 persons with a skin disorder. If 150 had been exposed
to the chemical A, 74 to the chemical B and 36 to both the chemicals
A and B,
Slide 6 : EXAMPLE 4 There are 260 persons with a skin disorder. If 150 had been exposed
to the chemical A, 74 to the chemical B and 36 to both the chemicals
A and B, find the number of persons exposed to
Slide 7 : EXAMPLE 4 There are 260 persons with a skin disorder. If 150 had been exposed
to the chemical A, 74 to the chemical B and 36 to both the chemicals
A and B, find the number of persons exposed to 1. Chemical A but not chemical B;
Slide 8 : EXAMPLE 4 There are 260 persons with a skin disorder. If 150 had been exposed
to the chemical A, 74 to the chemical B and 36 to both the chemicals
A and B, find the number of persons exposed to 1. Chemical A but not chemical B;
2. Chemical B but not chemical A;
Slide 9 : EXAMPLE 4 There are 260 persons with a skin disorder. If 150 had been exposed
to the chemical A, 74 to the chemical B and 36 to both the chemicals
A and B, find the number of persons exposed to 1. Chemical A but not chemical B;
2. Chemical B but not chemical A;
3. Chemical A or chemical B.
Slide 10 : SOLUTION: Let U = set of all persons with skin disorder;
Slide 11 : SOLUTION: Let U = set of all persons with skin disorder;
Slide 12 : SOLUTION: Let U = set of all persons with skin disorder; U
Slide 13 : SOLUTION: Let U = set of all persons with skin disorder; U
Slide 14 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A
Slide 15 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A
Slide 16 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A U A
Slide 17 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B
Slide 18 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B
Slide 19 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A U A B = set of all persons exposed to the chemical B B
Slide 20 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B A n B = set of all persons exposed to both the
chemicals A and B
Slide 21 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A U A B = set of all persons exposed to the chemical B B A n B = set of all persons exposed to both the chemicals A and B
Slide 22 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A U A B = set of all persons exposed to the chemical B B A n B = set of all persons exposed to both the chemicals A and B A n B
Slide 23 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A U A B = set of all persons exposed to the chemical B B A n B
Slide 24 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A n (U) = 260 n (A) = 150 B = set of all persons exposed to the chemical B n (B) = 74 n(A n B)
=36
Slide 25 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A n (U) = 260 n (A) = 150 B = set of all persons exposed to the chemical B n (B) = 74 n(A n B)
=36 That is, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36.
Slide 26 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. (i) Set of persons exposed to chemical A but not B = (A – B)
Slide 27 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. (i) Set of persons exposed to chemical A but not B = (A – B) n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 A - B
Slide 28 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 A - B Now, n (A – B) + n (A B) = n (A) (i) Set of persons exposed to chemical A but not B = (A – B)
Slide 29 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 A - B Now, n (A – B) + n (A B) = n (A) n(A – B)=n (A) – n(A B)
= 150 – 36 = 114. (i) Set of persons exposed to chemical A but not B = (A – B)
Slide 30 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 (ii) Set of persons exposed to chemical B but not A = (B – A)
Slide 31 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 B – A (ii) Set of persons exposed to chemical B but not A = (B – A)
Slide 32 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 B – A Now, n (B – A) + n (A B) = n (B) (ii) Set of persons exposed to chemical B but not A = (B – A)
Slide 33 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 B – A Now, n (B – A) + n (A B) = n (B) n (B – A)
= n (B) – n (A B)
= 74 – 36 = 38 (ii) Set of persons exposed to chemical B but not A = (B – A)
Slide 34 : Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 B – A A - B (iii) Set of persons exposed to chemical A or B = A B n (A B) = n (A) + n (B) – n (A B)
Slide 35 : Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 B – A A - B (iii) Set of persons exposed to chemical A or B = A B n (A B) = n (A) + n (B) – n (A B) = 150 + 74 – 36 = 188
Slide 36 : Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. n (U) = 260 n (A) = 150 n (B) = 74 n(A n B)
=36 B – A A - B (iii) Set of persons exposed to chemical A or B = A B n (A B) = n (A) + n (B) – n (A B) = 150 + 74 – 36 = 188
Slide 37 : SOLUTION: Let U = set of all persons with skin disorder; A = set of all persons exposed to the chemical A B = set of all persons exposed to the chemical B Then, n (U) = 260, n (A) = 150, n (B) = 74, and n (A B) = 36. (i) Set of persons exposed to chemical A but not B = (A – B) Now, n (A – B) + n (A B) = n (A) n (A – B) = n (A) – n (A B) = 150 – 36 = 114. Number of persons exposed to chemical A but not B = 114.
Slide 38 : (iii) Set of persons exposed to chemical A or B = A B n (A B) = n (A) + n (B) – n (A B) = 150 + 74 – 36 = 188 Number of persons exposed to chemical A or chemical B = 38. (ii) Set of persons exposed to chemical B but not A = (B – A) Now, n (B – A) + n (A B) = n (B) n (B – A) = n (B) – n (A B) = 74 – 36 = 38 Number of persons exposed to chemical B but not A = 38.