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 1**

^{st}questionSo, the relation is proved.

**For 3**

^{rd}questionLet

*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!

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