Can someone please help me with this I am not getting the same answers as the examples in the book.

U={1,2,3,4,5,6,7,8}
A={1,2,3,4,7,8}
B={1,2,4,5}

Determine (A'UB')n(AUB)'

A' = {5,6)

B' = {3,6,7,8}
(A'UB') = {3,5,6,7,8}

(AUB)' = {6}

I don't understand the operator n
is it supposed to stand for "intersection" ?

if so, then

(A'UB') ∩ (AUB)' = {6}

if not, let me know what the n stands for

yeah, u r very correct. n stands for intersection. ans=6

yes Reiny it stands for intersection thank your help.

f(x)= X2- 6x - 8

To solve this problem, we need to understand and apply the set operations and principles. Here's how you can approach it step-by-step:

Step 1: Understand the notations used:
- A' represents the complement of set A, which means all elements that are not in set A.
- U represents the universal set, which is the set containing all possible elements.
- n represents the intersection, which means finding the common elements between two sets.
- U represents the union, which means combining the elements of two sets without duplication.

Step 2: Find A' (complement of set A):
To find A', you need to identify all the elements that are not present in set A but are in the universal set U. In this case, A = {1,2,3,4,7,8}.
- So, A' = {5,6} (elements of U not present in A)

Step 3: Find B' (complement of set B):
To find B', you need to identify all the elements that are not present in set B but are in the universal set U. In this case, B = {1,2,4,5}.
- So, B' = {3,6,7,8} (elements of U not present in B)

Step 4: Find A'UB':
- To find A'UB', you need to find the union of A' and B'.
- A'UB' = {5,6} U {3,6,7,8} = {3,5,6,7,8}

Step 5: Find AUB':
- To find AUB', you need to find the union of sets A and B'.
- AUB' = {1,2,3,4,7,8} U {3,6,7,8} = {1,2,3,4,6,7,8}

Step 6: Find (AUB)' (complement of AUB):
- To find (AUB)', you need to identify all the elements that are not present in set AUB but are in the universal set U. In this case, AUB = {1,2,3,4,6,7,8}.
- So, (AUB)' = {5}

Step 7: Find (A'UB')n(AUB)':
- To find (A'UB')n(AUB)', you need to find the intersection of (A'UB') and (AUB)'.
- (A'UB')n(AUB)' = {3,5,6,7,8} n {5} = {}

Therefore, the answer is an empty set (no common elements).

I hope this explanation helps you understand how to solve this problem step-by-step. If you have any further questions, feel free to ask!