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Chapter: 9th Maths : UNIT 1 : Set Language

Exercise 1.5: De Morgan’s Laws

Maths : Set Language : Book Back, Exercise, Example Numerical Question with Answers, Solution: Exercise 1.5: De Morgan’s Laws

Exercise 1.5

1. Using the adjacent Venn diagram, find the following sets:


 (i) A − B (ii) B -C (iii) A′ B′  (iv) A′ ∩ B′ (v) (B C)′  (vi) A − (B C) (vii) A − (B ∩C)



2. If K = { a , b, d, e, f } , L = { b, c, d, g } and M = { a , b, c, d, h } , then find the following:

(i) K (L ∩ M) (ii) K ∩ (L M) (iii) (K L ) ∩ (K M) (iv) (K∩ L) (K ∩ M)

 and verify distributive laws.



3. If A = {x : x , − 2 < x ≤ 4}, B={x : x W , x ≤ 5}, C = {−4, −1, 0, 2, 3, 4}, then  verify A (B ∩C ) = (A B ) ∩ (A C) .



4. Verify A (B ∩C ) = (A B ) ∩ (A C) using Venn diagrams.



5. If A = {b, c, e, g, h} , B = {a , c, d , g, i } and C = {a , d, e, g, h} , then show that A(B C) = (AB)(AC).



6. If A = {x : x = 6n, nW and n<6}, B = {x : x = 2n, n and 2<n9} and C = {x : x = 3n, n and 4n<10}, then show that A (B C ) = (A B ) (A C)




7. If A = {–2,0,1,3,5}, B = {–1,0,2,5,6} and C = {–1,2,5,6,7}, then show that A (B C) = (AB)(AC).



8. If A = {y : y = [a + 1] /2 , aW and a ≤ 5}, B = {y : y = [2n -1] / 2, nW and n < 5} and  C = {-1, -1/2,1,3/2,2}, then show that A − (B C ) = (A − B ) ∩ (A −C) .



9. Verify A (B C ) = (A B ) (A C) using Venn diagrams.



10. If U = {4,7,8,10,11,12,15,16}, A={7,8,11,12} and B = {4,8,12,15} then verify De Morgan’s Laws for complementation.



11. Verify (A ∩ B)′ = A′ B′ using Venn diagrams.



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