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(a) Suppose A, B and D are sets with the following properties: A ∩ B =...

(a) Suppose A, B and D are sets with the following properties:
A ∩ B = A,     B ∩ D = D        ,   ( Ac ∪ Dc)c = ∅
    Draw a venn diagram for these sets and hence shade the region
                                                      ( Ac \ Bc) ∩ Dc    
(b)   Given that P(A U B) = k, P( A ) = 0.4, P( B ) = 0.2, determine the value of k if
      (i)    A and B are independent. (ii)   A and B are mutually exclusive. (iii) B is contained in A.

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