I need the following questions answer. Please help me. If anyone solves for me it will be so humble for me. 1.Draw the Venn diagram of AՍ(BՈC) 2. A company studies the product preferences of 25000 customers. It was found that each of the product A, B, C was liked by 7420, 6250 and 5990 respectively and all the products were liked by 1400; products A & B were liked by 2570, products A and C were liked by 1150 and products B and C were liked by 1950. Prove that the results are not correct. 3. Find the equation of the line passing through the following points: (4,6) and (-3,7). 4. Show that the points (0, 3), (-2,1) and (-1, 4) are the vertices of a right-angled triangle. 5.Suppose two sets are defined as: X={1, 2, 3} and Y={a, b, c, d}. Find which are functions? (i) F1={(1, a), (2, a), (3, a)} (ii) F2={(1, a), (1, b), (2, c), (3, d)} 6.Find the domain and range of the function f(x)= 2+4 7. Solve the equation graphically: 12x-7y=-6 5x-7y=27 8 . A person named Rafiq’s annual income has increased for Tk. 3500 but there is no charge in the income tax payable for him since the rate of income tax has been reduced from 7% to 4%. Find his present income.
Answers
Given : A company studies the product preferences of 25000 customers. It was found that each of the product A, B, C was liked by 7420, 6250 and 5990 respectively and all the products were liked by 1400; products A & B were liked by 2570, products A and C were liked by 1150 and products B and C were liked by 1950
To Find : Prove that the results are not correct.
Solution:
A = 7420
B = 6250
C = 5990
A∩B∩C = 1400
A ∩ B = 2570
A ∩ C = 1150
B ∩ C = 1950
A∩B∩C = 1400 > A ∩ C = 1150
Which is not possible as
A∩B∩C ≤ A ∩ C
because if we calculate who like A & C only
Then A ∩ C - A∩B∩C
= 1150 - 1400
= -250
( which is not possible )
Hence proved that result are not correct
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