QuestionНайдите $n(B)$ , если $n(A \cup B)=31$ , $n(A)=18$ , $n(A \cap B)=9$ .

Studdy Solution

STEP 1

Assumptions1. The total number of elements in the union of sets A and B, denoted as $n(A \cup B)$ , is31. . The total number of elements in set A, denoted as $n(A)$ , is18.
3. The total number of elements in the intersection of sets A and B, denoted as $n(A \cap B)$ , is9.

STEP 2

We need to find the total number of elements in set B, denoted as $n(B)$ . We can use the formula for the number of elements in the union of two sets.
$n(A \cup B) = n(A) + n(B) - n(A \cap B)$

STEP 3

We can rearrange the formula to solve for $n(B)$ .
$n(B) = n(A \cup B) - n(A) + n(A \cap B)$

STEP 4

Now, plug in the given values for $n(A \cup B)$ , $n(A)$ , and $n(A \cap B)$ to calculate $n(B)$ .
$n(B) =31 -18 +9$

STEP 5

Calculate the total number of elements in set B.
$n(B) =31 -18 +9 =22$ The total number of elements in set B is22.

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