Question

let A and B two finite sets such that n(A) =20 and n(B)= 28 and n(AuB)= 36 . find n(A n B)

Answer 1

Hey

Here is your answer,

Given that,

n(A) = 20
n(B) = 28
n(A U B ) = 36

n (A n B) = n(A) + n(B) - n(A U B)
= 20 + 28 - 36
= 48-36
= 12

Hope it helps you!

Answer 2

Answer:

Concept:

A U B (which can be read as "A or B" (or) "A union B") denotes the union of two sets A and B, a set that includes all of the elements of both sets A and B. The union of two sets A and B is calculated using the union B formula. Simply grouping all the components of A and B into one set and eliminating duplicates will reveal the union. In other words, A U B can also be calculated without utilising the A union B formula.

Step-by-step explanation:

Given:

$n(A)=20$

$n(B)=28$

$n(A\cup B)=36$

To find:

$n(A\cap B)$

Solution:

• By concept,

$n(A \cup B)$ = Number of elements in A or B

$n(A)$ = Number of elements in A

$n(B)$ = Number of elements in B

$n(A\cap B)$= Number of elements that are common to both A and B

• By the formula,

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

Substituting given values,

$36=20+28-n(A\cap B)$

$n(A\cap B)=20+28-36$

                $=48-36$

                $=12$

Hence, $n(A\cap B)=12$

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