Question

n(A∩B) + n(AUB) =n(A)+n(B).​

Answer 1

Answer:

,

Step-by-step explanation:

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Answer 2

Answer:

From the venn diagram, element of set A are {1, 2, 3, 4, 5} and of set B are {2, 5, 6, 7, 9}.

Step-by-step explanation:

To prove :-

n(A∩B) + n(AUB) =n(A)+n(B).

Solution :-

In order to prove this statement, we should know about intersection and union of set.

Intersection of sets (∩) is the common elements between two sets whereas union of sets (U) is the set containing elements of both the sets i.e. union is basically the sum of two sets.

Clearly from given Venn diagram :-

• (A ∩ B) = {2,5}
• (A U B) = {1, 2, 3, 4, 5, 6, 7, 9}

Number of elements in union and intersection :-

• n(A ∩ B) = 2
• n(A U B) = 8

Number of elements in set A and set B :-

• n(A) = 5
• n(B) = 5

We have to prove :-

n(A∩B) + n(AUB) =n(A)+n(B).

Substitute values ::

→ 2 + 8 = 5 + 5

→ 10 = 10

Hence given equation is proved