Question

A and B be two sets containing 12 and 27 distinct elements respectively. what can be the minimum number of elements in AUB ? also find the maximum number of elements in AUB?

please help me to solve this.
class 11 maths ch1 sets​

Answer 1

Answer:

If A and B are two sets containing 3 and 6 elements respectively, what can be the minimum number of elements in A ∪ B ? How can you find the maximum number of elements in A ∪ B?

n(A)=3

n(B)=6

n(A∪B)=n(A)+n(B)−n(A∩B)

Now we have already given n(A)=3 and n(B)=6

So n(A∪B) can be minimum when n(A∩B) is maximum or these two sets have maximum overlapping or in other words maximum elements in common. A and B can have atmost 3 elements common.

Then minimum no. of elements of A∪B can be achieved only when A⊂B . Note here it is proper subset symbol.

So, min(n(A∪B))=n(A)+n(B)−max(n(A∩B))=6+3−3=6

Now max value can be achieved when n(A∩B) is minimum or n(A∩B)=0

max(n(A∪B))=n(A)+n(B)−min(n(A∩B))=6+3−0=9

Answer 2

Answer:

Thankyou for giving me Thanks