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.
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!