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D Divya Prakash Singh
Universal set = U = {1,2,3,4,5,6,7....................} (i) {x : x is an even natural number} = {2,4,6,8,..........}    {x : x is an even natural number}'= U - {x : x is an even natural number}  = {1,3,5,7,9,..........} = {x : x is an odd natural number} (ii) { x : x is an odd natural number }' = U - { x : x is an odd natural number } = {x : x is an even natural number} (iii)  {x : x is a...

D Divya Prakash Singh
The following are the answers for the questions (i) A  A′  U (ii) ′  A   A (iii) A  A′   (iv) U′  A

D Divya Prakash Singh
A' is the set of all triangles whose angle is  in other words A' is set of all equilateral triangles.

D Divya Prakash Singh
(i) (A ∪ B)′ (A ∪ B) is in yellow colour (A ∪ B)′ is in green colour ii) A′ ∩ B′ is represented by the green colour in the below figure   iii) (A ∩ B)′ is represented by green colour in the below diagram and white colour represents (A ∩ B) iv)  A′ ∪ B′ The green colour represents   A′ ∪ B′

D Divya Prakash Singh
U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7} (i) (A  B)′ = A′ B′ L.H.S = (A  B)′ = U - (A  B) = {1,9} R.H.S =  A′ B′ = {1,3,5,7,9}  {1,4,6,8,9} = {1,9} L.H.S = R.H.S Hence,the statement is true. (ii) (A  B)′ = A′  B′   L.H.S = U - (A  B) ={1,3,4,5,6,7,8,9}  R.H.S =  A′  B′ = {1,3,5,7,9}  {1,4,6,8,9} = {1,3,4,5,6,7,8,9}   L.H.S = R.H.S Hence,the statement is true.

D Divya Prakash Singh
Universal set = U = {1,2,3,4,5,6,7,8.............} (vi) { x : x is a perfect square }' = U - { x : x is a perfect square } =  { x : x  N and x is not a perfect square } (vii) { x : x is a perfect cube}' = U - { x : x is a perfect cube} =  { x : x  N and x is not a perfect cube} (viii) { x : x + 5 8 }' = U - { x : x + 5 8 } = U - {3} = { x : x N and x  3 } (ix) { x : 2x + 5 9}' = U - { x : 2x +...