If ξ = {x | x ϵ N, x ≤ 12}, A = {prime numbers} and B = {odd numbers}

If ξ = {x | x ϵ N, x ≤ 12}, A = {prime numbers} and B = {odd numbers}, then
(i) Find A ∪ B and A ∩ B.
(ii) Verify that n(A ∪ B) + n(A ∩ B) = n(A) + n(B).
(iii) Find A’ and B’.
(iv) Find (A ∪ B)’ and verify that n(A ∪ B) + n(A ∪ B)’ = n(ξ).
(v) Find (A ∩ B)’ and A’ ∪ B’. Are they equal ?

Solution:

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