Respuesta :
Answer:
Option c - [tex]n(A^c\cup B)=125[/tex]
Step-by-step explanation:
Given : Suppose that n(U) = 200, n(A) = 105, n(B) = 110, and n(A∩B) = 30.
To find : The value of [tex]n(A^c\cup B)[/tex] ?
Solution :
n(U) = 200, n(A) = 105, n(B) = 110, and n(A∩B) = 30
We know that,
[tex]n(A^c)=n(U)-n(A)[/tex]
[tex]n(A^c)=200-105[/tex]
[tex]n(A^c)=95[/tex]
and [tex]n(A^c \cap B)=n(B)-n(A\cap B)[/tex]
[tex]n(A^c \cap B)=110-30[/tex]
[tex]n(A^c \cap B)=80[/tex]
Now, [tex]n(A^c\cup B)=n(A^c)+n(B)-n(A^c \cap B)[/tex]
[tex]n(A^c\cup B)=95+110-80[/tex]
[tex]n(A^c\cup B)=125[/tex]
Therefore, option c is correct.
The value of the union set given as n(A^c U B) is; C: 125
What is the union of the set?
We are given;
n(U) = 200, n(A) = 105, n(B) = 110, and n(A ∩ B) = 30.
In sets, we know that complement of set A is;
n(A^c) = n(U) - n(A)
Thus; n(A^c) = 200 - 105
n(A^c) = 95
Also, we know that;
n(A^c ∩ B) = n(B) - n(A ∩ B)
n(A^c ∩ B) = 110 - 30
n(A^c ∩ B) = 80
Thus;
n(A^c U B) = n(A^c) + n(B) - n(A^c ∩ B)
n(A^c U B) = 95 + 110 - 80
n(A^c U B) = 125
Read more about Union of Sets at; https://brainly.com/question/1563195
