Question
A={1,3,6,9},B={4,5,6,9},C={x:5<x<_9} are subset of the universal set U = {1,2,3,4,5,6,7,8,9} Find:
(I) A n (B n C)
(II)(A U B)n(B U C)
(I) A n (B n C)
(II)(A U B)n(B U C)
Answers
Answered by
oobleck
well, you know that 5 < x ≤ 9 so x is an element of {6,7,8,9}
(A U B) n (B U C) = {1, 3, 4, 5, 6, 9} n {4, 5, 6, 9, 6, 7, 8, 9} = {4,5,6,9}
(A U B) n (B U C) = {1, 3, 4, 5, 6, 9} n {4, 5, 6, 9, 6, 7, 8, 9} = {4,5,6,9}
Answered by
GPT 3.5
(I) A n (B n C)
To find the intersection of sets, we need to find elements that are common to all sets.
B n C = {6, 9} (since 6 and 9 are the only elements in both set B and set C)
A n (B n C) = {1, 3, 6, 9} n {6, 9} = {6, 9}
Therefore, A n (B n C) = {6, 9}.
(II) (A U B) n (B U C)
To find the union of sets, we combine all elements from both sets.
A U B = {1, 3, 4, 5, 6, 9} (as it contains all elements from both sets A and B)
B U C = {4, 5, 6, 9, x: 5 < x ≤ 9} (as it contains all elements from set B and any element between 5 and 9)
(A U B) n (B U C) = {1, 3, 4, 5, 6, 9} n {4, 5, 6, 9, x: 5 < x ≤ 9}
Simplifying this expression requires additional information about the specific value of "x" within the given condition. Without that information, the intersection cannot be determined precisely.
To find the intersection of sets, we need to find elements that are common to all sets.
B n C = {6, 9} (since 6 and 9 are the only elements in both set B and set C)
A n (B n C) = {1, 3, 6, 9} n {6, 9} = {6, 9}
Therefore, A n (B n C) = {6, 9}.
(II) (A U B) n (B U C)
To find the union of sets, we combine all elements from both sets.
A U B = {1, 3, 4, 5, 6, 9} (as it contains all elements from both sets A and B)
B U C = {4, 5, 6, 9, x: 5 < x ≤ 9} (as it contains all elements from set B and any element between 5 and 9)
(A U B) n (B U C) = {1, 3, 4, 5, 6, 9} n {4, 5, 6, 9, x: 5 < x ≤ 9}
Simplifying this expression requires additional information about the specific value of "x" within the given condition. Without that information, the intersection cannot be determined precisely.
Answered by
GPT 3.5
Yes, you are correct. I apologize for overlooking that information. Given that 5 < x ≤ 9 and x is an element of {6,7,8,9}, the intersection of (A U B) and (B U C) is indeed {4, 5, 6, 9}. Thank you for providing that clarification.