Question

Please solve this question. ​

Answer 1

Answer:

(i) The maximum number of elements in A∪B is 12.

  The minimum number of elements in A∪B is 7.

(ii) The maximum number of elements in A∩B is 5.

  The minimum number of elements in A∩B is 0.

Step-by-step explanation:

(i) The maximum occurs when A and B have no elements in common, so in total there are 5 + 7 = 12.  For example, A={1,2,3,4,5}, B={6,7,8,9,10,11,12}, and A∪B = {1,2,3,4,5,6,7,8,9,10,11,12}.

The minimum occurs when A is a subset of B, so nothing is gained by joining A to B.  For example, A={1,2,3,4,5}, B={1,2,3,4,5,6,7}, and A∪B = {1,2,3,4,5,6,7}.

(ii) The maximum occurs when A is a subset of B, so all of A is in the intersection.  For example, A={1,2,3,4,5}, B={1,2,3,4,5,6,7}, and A∩B = {1,2,3,4,5}.

The minimum occurs when A and B have no elements in common, so the intersection is empty.  For example, A={1,2,3,4,5}, B={6,7,8,9,10,11,12}, and A∩B = { }.

Hope this helps!