Let M be the set of all students take part in music.
Let D be the set of all students take part in drama.
n( M) = 25, n(D) = 30 and n(M\(\cap \)D) = 8
By using venn diagram
From the venn diagram we get.
(i) Number of students take part in only music = 17
(ii) Number of students take part in only drama = 22
(iii) Total number of students in the class = 17 + 8 + 22 = 47

Alter :
(i) The number of students who take part in only music
= n(M) - n(M\(\cap \)D)
= 25 - 8 = 17
(ii) The number of students who take part in only drama
= n(D) - n(M\(\cap \)D)
= 30 - 8 = 22
(iii) The total number of students
n(M∪D) = n(M) + n(D) - n(M\(\cap \)D)
= 25 + 30 - 8 = 47

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 3, 4, 8, 10}; B = {1, 2, 5, 8, 10}
n(U) = 10, n(A) = 5, n(B) = 5
(A\(\cup \)B) = {2, 3, 4, 8, 10} \(\cup \) {1, 2, 5, 8, 10}
= {1, 2, 3, 4, 5, 8, 10}
\(\therefore\) n(A\(\cup \)B) = 7
(A\(\cap \)B) = {2, 3, 4, 8, 10} \(\cap \) {1,2,5,8,10}
= { 2, 8, 10}
n(A\(\cap \)B) = 3 .............(1)
n(A) + n(B) -n(A\(\cap \)B) = 5 + 5 - 3
= 10 - 3
= 7 .......(2)
From (1) and (2) we get,
n(A\(\cup \)B) = n(A) + n(B) - n(A\(\cap \)B)

n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B') = 350
n(A∪B) = n(A) + n(B) - n(A∩B)
500 = 300 + n(B) - 50
500 = 250 + n(B)
500 - 250 = n(B)
250 = n(B)
\(\therefore\) n(B) = 250
n(U) = n(B) + n(B)'
= 250 + 350
= 600
\(\therefore\) n(B) = 250 and n(U) = 600

n(A) = 25, n(B) = 40, n(AUB) = 50 and n(B') = 25
n(A\(\cap\)B) = n(A) + n(B) - n(AUB)
n(A\(\cap\)B) = 25 + 40 - 50
= 65 - 50
= 15
n(U) = n(B) + n(B)'
= 40 + 25
= 65
\(\therefore\) n(A\(\cap\)B) = 15 and n(U) = 65

Let A be the set of people owned car A
Let B be the set of people owned car B
n( A) = 400, n(B) = 200, n(A \(\cap\) B) = 50
n(A \(\cup\) B) = 500 .........(1)
n(A) + n(B) - n(A \(\cap\) B) = 400 + 200 - 50
= 600 - 50
= 550  ...........(2)
From (1) and (2) we get
\(n(A\cup B)\ne n(A) +n(B)-n(A\cap B)\)
\(\therefore\) The given data is incorrect.

Let the people who like tea be T. 
Let the people who like coffee be C 
By using formula 
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
(i) n(T ∩ C) = n(T) + n(C) – n(T ∪ C) = 35 + 20 – 45 = 55 – 45 = 10 
The number of people who like both coffee and tea = 10.
(ii) The number of people who do not like tea 
n(T) = n(U) – n(T) = 45 – 35 = 10
(iii) The number of people who do not like coffee 
n(C) = n(U) – n(C) = 45 – 20 = 25.

a = 600 - (120 -x + x + 80 -x)
= 600 - (200 -x)
= 600 - 200 + x = 400 + x
b = 350 - (120 -x + x + 100 -x)
= 350 - (220 - x)
= 350 - 230 + x = 130 + x
c = 280 - (80 - x + x + 100 - x)
2800 - (180 -x)
= 280 - 180 + x = 100 + x
Each farmer grew atleast one of the above three, the number of farmers who grew all the three is x.
= a + b + c + 120 - x + 100 - x + 80 - x + x = 1000
400 + x + 130 + x + 100 + x + 120 - x + 100 - x + 80 - x + x = 1000
ஃ 930 + x = 1000
x = 1000 - 930 = 70
ஃ 70 farmers grew all the three crops.

Tamil Newspaper buyers n(A) = 275
English Newspaper buyers n(B) = 150
Hindi Newspaper buyers n(C) = 45
n (A∪ B ∪ C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
Tamil and English Newspaper buyers n(A∩B) = 125
English and Hindi Newspaper buyers n(B∩C) = 17
Hindi and Tamil Newspaper buyers n(C∩A) = 5
All the three Newspaper buyers n(A∩B∩C) = 3

(i) Number of families buy only one newspaper = 148 + 11 + 26 = 185
(ii) Number of families buy atleast two news papers = 122 + 14 + 2 + 3 = 141
(iii) Total number of families in the colony = 148 + 11 + 26 + 122 + 14 + 2 + 3 = 326

(i) A-B = {3,4,6}
(ii) B-C = {-1,5,7}
(iii) A'UB'
A'UB'
A' = {1,2,0,-3,5,7,8}
B' = {-3,0,1,2,3,4,5,6}
A'UB' = {-3,0,1,2,3,4,5,6,7,8}
(iv) A'⋂B'
A'⋂B' = {-3,0,1,2}
(v) (BUC)'
BUC = {-3,-2,-1,0,3,5,7,8}
(BUC)' = U-(BUC)
= {-3,-2,-1,0,1,2,3,4,5,6,7,8} - {-3,-2,-1,0,3,5,7,8}
(BUC)' = {1,2,4,6}
(vi) A-(BUC) = {-2,-1,3,4,6} - {-3,-2,-1,0,3,5,7,8} = {4,6}
(vii) A-(B⋂C)
B⋂C = {-2,8}
A-(B⋂C) = {-2,-1,3,4,6} - {-2,8} = {-1,3,4,6}