Question

A city has three newspapers A, B and C. Of the adult population, 1% read none of these newspapers. 36% read A, 40% read B, 52% read C, 8% read A and B, 11% read B and C, 13% read A and C and 3% read all the three newspapers. Required:
i. Illustrate the above information on a venn diagram
ii. What percent of the adult population read newspaper A only
iii. What percent of the adult population read newspaper B or Newspaper C
iv. What percent of the adult population read newspaper A or B but not C

Answer 1

Answer on Question #56513 – Math – Discrete Mathematics

Question

A city has three newspapers A, B and C. Of the adult population, 1% read none of these newspapers. 36% read A, 40% read B, 52% read C, 8% read A and B, 11% read B and C, 13% read A and C and 3% read all the three newspapers. Required:

i. Illustrate the above information on a venn diagram

ii. What percent of the adult population read newspaper A only

iii. What percent of the adult population read newspaper B or Newspaper C

iv. What percent of the adult population read newspaper A or B but not C

Solution

i. Only A and B = (A and B) - (A and B and C) = 8% -- 3% = 5%.

Only B and C = (B and C) - (A and B and C) = 11% -- 3% = 8%.

Only A and C = (A and C) - (A and B and C) = 13% -- 3% = 10%.

Only A = A - (Only A and B) - (A and B and C) - (Only A and C) = 36% -- 5% -- 3% -- 10% = 18%.

Only B = B - (Only A and B) - (A and B and C) - (Only B and C) = 40% -- 5% -- 3% -- 8% = 24%.

Only C = C - (Only B and C) - (A and B and C) - (Only A and C) = 52% -- 8% -- 3% -- 10% = 31%.

ii. Only A = A - (Only A and B) - (A and B and C) - (Only A and C) = 36% -- 5% -- 3% -- 10% = 18%.

iii.

Method 1

B or C = B + C - (B and C) = 40% + 52% - 11% = 81%

(100% -- 1%) - 18% = 81%.

Method 2

B or C = 100% - None - Only A = 100% -- 1% - 18% = 81%.

iv. A or B but not C = Only B + (Only A and B) + Only A = 24% + 5% + 18% = 47%.

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