Question

When 25 students went to Washington dc 18 of them visited the museum of natural history and 22 visited the natural air and space museum. How many students visited both museums.

Answer 1

Answer:

15 students visited both museums.

Step-by-step explanation:

Operations With Sets

Sets are a collection of elements. Some sets have elements in common with other sets. These elements are said to be in their intersection. If we know the number of elements in the set A and in the set B, and also the total number of elements in both sets, we can say

$N(A\bigcup B)=N(A)+N(B)-N(A\bigcap B)$

where $N(A\bigcup B)$ is the total number of elements, N(A) and N(B) are the number of elements in A and B respectively, and $N(A\bigcap B)$ is the number of elements in their intersection. If we wanted to know that last number, then we isolate it

$N(A\bigcap B)=N(A)+N(B)-N(A\bigcup B)$

Let A= Students who visited the museum of natural history

B=Students who visited the natural air and space museum

We know $N(A)=18, N(B)=22, N(A\bigcup B)=25,\ so$

$N(A\bigcap B)=18+22-25=15$

Answer: 15 students visited both museums.

Note: We are assuming no students didn't visit at least one museum