Question

Let A and B be two sets containing 3 and 6 elements respectively find the maximum and minimum number of elements in a union b

Answer 1

$\underline{\underline{\mathfrak{\pink{Answer :-}}}}$

Maximum = 9

Minimum = 6

$\underline{\underline{\mathfrak{\pink{Explanation:-}}}}$

Given,

A and B are the two sets which contains 3 and 6 elements respectively

Therefore,

n(A) = 3

n(B) = 6

Maximum no. of elements in AUB

AUB wil be maximum when, the both A and B are Disjoint sets

To find Maximum no. of elements, we have to add the no. of elements of both sets

Therefore,

n(AUB) = n(A) + n(B)

n(AUB) = 3+6

n(AUB) = 9

Minimum no. of elements in AUB

AUB will be minimum, when A is a sub-set of B

If, A C B

Then,

n(AUB) = 6

Hence,

Maximum number of elements in AUB=9

minimum number of elements in AUB=6

Answer 2

Step-by-step explanation:

Given,

A and B are the two sets which contains 3 and 6 elements respectively

Therefore,

n(A) = 3

n(B) = 6

Maximum no. of elements in AUB

AUB wil be maximum when, the both A and B are Disjoint sets

To find Maximum no. of elements, we have to add the no. of elements of both sets

Therefore,

n(AUB) = n(A) + n(B)

n(AUB) = 3+6

n(AUB) = 9

Minimum no. of elements in AUB

AUB will be minimum, when A is a sub-set of B

If, A C B

Then,

n(AUB) = 6

Hence,

Maximum number of elements in AUB=9

minimum number of elements in AUB=6