Question

please tell me ans of question no 6​

Answer 1

Answer:

The maximum value that |A∪B| can take is 3+6 = 9.

E.g.  A = { 1, 2, 3 },  B = { 4, 5, 6, 7, 8, 9 }.  Then |A|=3, |B|=6 and |A∪B| = 9.

The minimum value that |A∪B| can take is 6.

E.g.  A = { 1, 2, 3 },  B = { 1, 2, 3, 4, 5, 6 }.  Then |A|=3, |B|=6 and |A∪B| = 6.

Step-by-step explanation:

Notice that

|A∪B| = |A| + |B| - |A∩B| = 3 + 6 - |A∩B| = 9 - |A∩B|

So to maximize |A∪B|, we need to minimize |A∩B|, and this is achieved when A and B are disjoint so that |A∩B| = 0.  Then |A∪B| = 9.

Meanwhile, to minimize |A∪B|, we need to maximize |A∩B|, and this is achieved when the smaller set, A, is a subset of the larger one, B, so that |A∩B| = |A| = 3.  Then |A∪B| = 9-3 = 6.