Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

* If [tex]$n(A)=80$[/tex] and [tex]$n(B)=65$[/tex], what is the least value of [tex][tex]$n(A \cup B)$[/tex][/tex]?

A. 125
B. 20
C. 80
D. 65

Sagot :

GinnyAnswer
To find the least value of [tex]\( n(A \cup B) \)[/tex], where [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are two sets, we can use the principle of set theory related to the union of two sets.

Given:
- [tex]\( n(A) = 80 \)[/tex]
- [tex]\( M(B) = 65 \)[/tex]

The least value of [tex]\( n(A \cup B) \)[/tex] occurs when there is no intersection between sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. In other words, when [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are disjoint sets.

For disjoint sets, the number of elements in the union is simply the sum of the number of elements in each set. Therefore, we perform the following:

[tex]\[ n(A \cup B) = n(A) + M(B) \][/tex]

Substituting the given values:

[tex]\[ n(A \cup B) = 80 + 65 \][/tex]

[tex]\[ n(A \cup B) = 145 \][/tex]

Thus, the least value of [tex]\( n(A \cup B) \)[/tex] is [tex]\( 145 \)[/tex].

None of the given options—125, 20, 80, or 65—are correct based on this calculation. The correct answer is [tex]\( 145 \)[/tex].
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.