Given that u = {1,2,3,4,5,6,7,8,9}, A ={2,3,4,5} and B= {4,5,7,8}, list the following sets:
i) Au (A1nB)
ii) Bu (A1n B)
iii) Au (AnB1)
iv) B1u (AnB1)
v) A u(A1nB1)
To list the sets, we need to apply the operations of union (u), intersection (n), and complement (1) to the given sets.
Given:
u = {1,2,3,4,5,6,7,8,9}
A = {2,3,4,5}
B = {4,5,7,8}
i) Au (A1nB)
To find this set, we start by taking the intersection of A and B, which gives us {4,5}.
Next, we take the union of u and the intersection of A and B.
So, Au (A1nB) = {1,2,3,4,5,6,7,8,9} u {4,5} = {1,2,3,4,5,6,7,8,9}.
ii) Bu (A1n B)
To find this set, we start by taking the intersection of A and B, which gives us {4,5}.
Next, we take the union of B and the intersection of A and B.
So, Bu (A1nB) = {4,5,7,8} u {4,5} = {4,5,7,8}.
iii) Au (AnB1)
To find this set, we start by taking the complement of B, which gives us {1,2,3,6,9}.
Next, we take the intersection of A and the complement of B.
So, Au (AnB1) = {2,3,4,5} u {1,2,3,6,9} = {1,2,3,4,5,6,9}.
iv) B1u (AnB1)
To find this set, we start by taking the complement of B, which gives us {1,2,3,6,9}.
Next, we take the intersection of A and B with their complements.
So, B1u (AnB1) = {4,5,7,8} u {1,2,3,6,9} = {1,2,3,4,5,6,7,8,9}.
v) A u(A1nB1)
To find this set, we start by taking the complement of A, which gives us {1,6,7,8,9}.
Next, we take the intersection of A complement, B complement, and the compliment of B intersect A.
So, A u(A1nB1) = {2,3,4,5} u ({1,6,7,8,9} n {1,2,3,6,9}) = {2,3,4,5} u {1,6,9} = {1,2,3,4,5,6,9}.
I hope this helps!