A={2,4,6,8}, B={2,3,7,9} and C={x:3<x<9} are subsets of the universal set.
U={2,3,4,5,6,7,8,9}, find
a. An(B¹nC¹)
b. (AuB)n(BuC)
a. An(B¹nC¹)
First, we need to find B¹ and C¹.
B¹ = U - B = {2, 4, 5, 6, 8}
C¹ = U - C = {2, 3, 4, 9}
Next, find the intersection of B¹ and C¹.
B¹nC¹ = {2, 4}
Now, find the intersection of A and B¹nC¹.
An(B¹nC¹) = A ∩ (B¹nC¹) = {2, 4}
Therefore, An(B¹nC¹) = {2, 4}.
b. (AuB)n(BuC)
First, find the union of A and B.
AuB = {2, 3, 4, 6, 7, 8, 9}
Next, find the union of B and C.
BuC = {2, 3, 4, 6, 7, 8, 9}
Now, find the intersection of AuB and BuC.
(AuB)n(BuC) = ({2, 3, 4, 6, 7, 8, 9}) ∩ ({2, 3, 4, 6, 7, 8, 9}) = {2, 3, 4, 6, 7, 8, 9}
Therefore, (AuB)n(BuC) = {2, 3, 4, 6, 7, 8, 9}.