In a town of $$10$$,$$000$$ families, it was found that $$40$$% families buy newspaper A, $$20$$% buy newspaper B and $$10$$% buy newspaper C. Also,$$5o$$ families buy newspapers A and B, $$3$$% buy newspapers B and C and $$4$$% buy newspapers A and C. lf $$2$$% families buy all the three newspapers, then number of families which buy newspaper A only is

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Infinity Learn · Accepted Answer

$$n(A)=40$$% of $$10$$,$$000=4$$,$$000n(B)=20$$% of $$10$$,$$000=2$$,$$000n(C)=10$$% of $$10$$,$$000=1$$,$$000n(A$$∩$$B)=5$$% of $$10$$,$$000=500n(B$$∩$$C)=3$$% of $$10$$,$$000=300n(C$$∩$$A)=4$$% of $$10$$,$$000=400n(A$$∩B∩$$C)=2$$% of $$10$$,$$000=200Number$$ of families which buy newspaper A $$only=nA$$∩Bc∩$$Cc=nA$$∩(B$$∪$$C)c=n(A)−n[A∩(B$$∪$$C)]$$=n(A)$$−n[(A$$∩$$B)∪(A$$∩$$C)]$$=n(A)$$−[$$n(A$$∩$$B)+n(A$$∩$$C)$$−$$n(A$$∩B∩$$C)$$]$$=4000$$−[$$500+400$$−$$200$$]$$=4000$$−$$700=3300$$

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