Question

n(A)=3,n(B)=6,then atleast how
many elements are there in (A U B)?
​

Answer 1

Answer:If n(A)=3 and n(B)=6, then how are the minimum and maximum elements in AUB?

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0≤n(A∩B)≤3.

So n(A∪B)=n(A)+n(B)−n(A∩B)⟹n(A∪B)=9−n(A∩B).

Minimum AUB elements condition: Out of 6 elements of set B, 3 elements are identical to that of set A. In this case AUB= B & it will have 6 elements

Maximum AUB elements condition: A & B are disjoint sets, that no element will be common to them. Then:

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

AUB has 9 elements.

⟹0≥−n(A∩B)≥−3⟹9+0≥9−n(A∩B)≥9−3⟹9≥9−n(A∩B)≥6⟹9≥n(A∪B)≥6

Answer 2

Answer:

{AUB}=9

Step-by-step explanation:

through

adding n{A} + n{B}