Others Maths Puzzle

PROVE THAT A (INTERSECTION)(B-C)= (A INTERSECTION B)-(A INTERSECTION C)

NOTE*= PROVE THIS WITHOUT TAKING ANY ARBITRARY ELEMENT..

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Others Other Question

Given 2 circles of radius R1 & R2. how many rotations will the smaller circle(radius R2) have to make for a full
revolution around the circle with radius R1?
there are ten children (aged 1 to 10 years)who have equal amounts of money. in the first transaction the eldest child gives one rupee to every child younger to him. in the second transaction , the second eldest child gives one rupee to every child younger to him.this type of distribution continues for the next two transactions. in the end the total sum with the children who have given money to other children is half the sum of money with children who did not give any money. what was the original amount with each child?
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