1 Prove A intersection (A U B)' = phi 2 Prove that if A U B - Maths - Sets

Question

1 Prove A intersection (A U B)' = phi
2 Prove that if A U B = C and A intersection B = phi, then C - B
= A
3 In ao town of 10,000 families it was found that 40% families
buy newspaper A, 20% families buy newspaper, 10% families buy
newspaper C, 5% buy A and B, 3% buy B and C, 4% buy A and C, If 2%
buy all three papers, then find the number of families which buy
newspaper A only

Sunanta Meitei · Accepted Answer

Hi! Here is the answer to your question For 1st question

So, the relation is proved For 3rd question Let A denote the set of families buying the newspaper A Let B denote the set of families buying the newspaper B Let C denote the set of families buying the newspaper C Then, by the given information, n (A) = 40% of 10,000 = 4000, n (B) = 20% of 10,000 = 2000, n (C) = 10% of 10,000 = 4000

Now, the given information can be represented using Venn diagram as,

From the diagram, it is clear that: Number of families which buy newspaper A only = n (A) – (300 + 200 + 200) = 4000 – 700 = 3300 Cheers!