Question

Set A and set B have 4 and 6 elements respectively what can be the minimum number of elementsin A ∪ B?

Answer 1

Answer:

6

Note:

★ Cardinal number of a set : The number of elements in a set is called its cardinal number.

• Cardinal number of a set A is denoted by n(A) .

★ Union of two sets : The union of two sets A and B is the set of all those elements which are either in A or in B or in both.

• This set is denoted by AUB .

• If A⊆B , then AUB = B .

★ Intersection of two sets : The intersection of two sets A and B is the set of all those elements which are in common in both A and B .

• This set is denoted by A⋂B .

• If A⊆B , then A⋂B = A .

Solution:

Here,

It is given that ;

n(A) = 4

n(B) = 6

The minimum number of elements in the set AUB will be 6 if A⊆B .

Moreover,

The maximum number of elements in the set AUB will be 10 if A and B are disjoint sets , ie ; A⋂B = ∅ .