if n(A)=25 and n(B)=15, find: (a) n(A u B)max, (b) n(Au B)min, (C) n(AnB)max, (d) n(A n B)min

if n(A)=25 and n(B)=15, find: (a) n(A u B)max,

(b) n(A u B)min, (C) n(A n B)max, (d) n(A n B)min
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1 Answer

I read this as set A has 25 elements and set B has 15 elements. 

(a) A∪B has a maximum of 25+15=40 elements meaning that B and A have no elements in common. Therefore max n(A∪B)=40.

(b) If B is a subset of A, min n(A∪B)=25.

(c) max n(A∩B)=15, if B is a subset of A.

(d) min n(A∩B)=0, if A and B have no common element.

 

 

by Top Rated User (788k points)

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