Question: 1.4.3 Let A l , . . . , A , be distinct subsets of S. (i) Find the maximum number of sets (including S

1.4.3 Let A l , . . . , A , be distinct subsets of S. (i) Find the maximum number of sets (including S and 0) of the smallest field containing A l l . . . A,. (ii) Find the maximum number of sets in this field if A,-1 c A,. (iii) Answer (ii) if A1 c A2 c

. . c A,. (iv) Answer (ii) if A1 = . . . = A , = 0. (v) Answer (i)-(iv) for a a-field.

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