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In this paper, upper and lower bounds each of the form c2*/0 are obtained for the maximum possible size of a collection Q of subsets of an it element set satisfying the restriction that no four distinct members A, B, C, D of Q satisfy AUB = C and AnB=D. The lower bound is obtained by a construction while the upper bound is obtained by applying a somewhat weaker condition on Q which leads easily to a bound. Probably there is an absolute constant c so that max 1 Q 1 = ~2~/&* + 0(2*/#) but we cannot prove this and have no guess at what the value of c is.

On collections of subsets containing no 4-member Boolean algebra.