Question

1. If n(A) = 40, n(B) = 60 and n(AUB) = 80, then find the value of n(A∩B), no(A) and no(B). Also, represent the above information in the Venn-diagram.

Answer 1

Answer:

n (A) - 40

n(b)- 60

n(AUB) -80

so find out the value of n(AnB)

easy question but first tell me that of which value of we have to tell its not clear

Answer 2

Answer:

Concept:

The cardinal number of a set is the number of unique elements or members of a finite set. In essence, cardinality allows us to specify a set's size. n(A), where A is any set and n(A) is the number of members in set A, is used to represent the cardinal number of a set.

Step-by-step explanation:

Given:

n(A) = 40, n(B) = 60 and n(AUB) = 80

Find:

n(A∩B), no(A) and no(B).
Solution:

We know that for any two finite sets A and B,

$n(A \cup B)=n(A)+n(B)-n(A \cap B).$

Here, it is given that $n(A)=40, n(B)=60$ and $n(A \cup B)=80$, therefore,

                        $\begin{aligned}&\mathrm{n}(\mathrm{A} \cup \mathrm{B})=\mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})-\mathrm{n}(\mathrm{A} \cap \mathrm{B}) \\\\&\Rightarrow 80 = 40+60-\mathrm{n}(\mathrm{A} \cap \mathrm{B}) \\\\&\Rightarrow 80 = 100-\mathrm{n}(\mathrm{A} \cap \mathrm{B}) \\\\&\Rightarrow \mathrm{n}(\mathrm{A} \cap \mathrm{B})=100-80 \\\\&\Rightarrow \mathrm{n}(\mathrm{A} \cap \mathrm{B})=20\end{aligned}$

             n(A) = n(A – B) + n(A ∩ B)

                     = n(40-60) + 20

                     = -20+20

              n(A) = 0

               n (B) = n (B – A) + n (A ∩ B)

                        = n(60-40) + 20

                       = 20 + 20

                   n(B) = 40

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