Question

Given the sets A=\ 0,1,3\ , B=\ 1,4,5\ , and C=\ 0,1,3,4,5\ , what is A n B n C

Answer 1

The intersection of sets A, B, and C, represented as A n B n C, is the set containing elements common to all three sets. In this case, the only element common to all three sets is the number 1. Therefore, the answer is {1}.

Step-by-step explanation:

The question involves finding the intersection of three sets A, B, and C. The intersection of sets A, B, and C, denoted as A ∩ B ∩ C, includes all elements that are common to all three sets. By examining each set, we can determine which numbers appear in all three.

Set A = {0, 1, 3}, Set B = {1, 4, 5}, and Set C = {0, 1, 3, 4, 5}. When we look for common elements, we notice that the number 1 appears in all three sets. Hence, the intersection of sets A, B, and C is {1}.

Therefore, A ∩ B ∩ C = {1}.

Answer 2

You have the following sets:

`\begin{gathered} A=\mleft\lbrace0,1,3\mright\rbrace \\ B=\mleft\lbrace1,4,5\mright\rbrace \\ C=\mleft\lbrace0,1,3,4,5\mright\rbrace \end{gathered}`

You can sketch a Venn diagram to determine the shared elements between the sets:

From the Venn diagram you can determine the elements that are shared by each set:

The sets A and C share the elements: A∩C= {0,3}

The sets B and C share the elements: B∩C= {4,5}

The sets A and B share no elements: A∩B= ∅

The three sets share one element so that: A∩B∩C= {1}