Given, U = {1,2,3,4,5,6,7,8,9,10,12,24}
A = {2,3,5,7}
B = {1,2,3,4,5,6,8,12,24}
Now, A’ = {1,4,6,8,9,10,12,24}
B’ = {5,7,9,10}
A ∪ B = {1,2,3,4,5,6,7,8,12,24}
(A ∪ B)’ = {9,10}
A ∩ B = {2,3}
(A ∪ B)’ = {1,4,5,6,7,8,9,10,12,24}
(i) A – B = A ∩ B’
L.H.S = A – B = {2,3,5,7} – {1,2,3,4,6,8,12,24} = {5,7}
R.H.S = A ∩ B’ = {2,3,5,7} ∩ {5,7,9,10} = {5,7}
∴ L.H.S = R.H.S,
(ii) (A ∪ B)’ = A ∩ B’
L.H.S = (A ∪ B)’ = {9,10}
R.H.S = A’∩ B’ = {1,4,6,8,9,10,12,24} ∩ {5,7,9,10} = {9,10}
∴ L.H.S = R.H.S,
(iii) (A ∩ B)’ = A’ ∩ B’
L.H.S = (A ∩ B)’ = {1,4,5,6,7,8,9,10,12,24}
R.H.S = A’ ∩ B’ = {1,4,6,8,9,10,12,24} ∩ {5,7,9,10} = {1,4,5,6,7,8,9,10,12,34}
∴ L.H.S = R.H.S,