If A 4,5,7,8,10), B={4, 5, 9) and C={1, 4, 6,9).
Find A (BUC) and (AB)~(AC)
A (BUC) is the union of B and C with elements that are also in A. So, A (BUC) = {4, 5, 9}.
(AB)~(AC) is the intersection of AB and AC. AB is the set of elements that are in both A and B, and AC is the set of elements that are in both A and C. So, (AB)~(AC) = {4}.
To find A (BUC), we need to combine the elements of set B and C into set A.
Step 1: Let's combine sets B and C: BUC = {4, 5, 9} U {1, 4, 6, 9} = {1, 4, 5, 6, 9}.
Step 2: A (BUC) means finding the intersection of set A and the combined set BUC.
A (BUC) = A ∩ (BUC) = {4, 5, 7, 8, 10} ∩ {1, 4, 5, 6, 9} = {4, 5}.
Therefore, A (BUC) = {4, 5}.
To find (AB)~(AC), we need to find the difference between the intersection of sets A and B and the intersection of sets A and C.
Step 1: Find intersection of sets A and B: A ∩ B = {4, 5}.
Step 2: Find intersection of sets A and C: A ∩ C = {4}.
Step 3: Take the difference between A ∩ B and A ∩ C: (AB)~(AC) = A ∩ B - A ∩ C = {4, 5} - {4} = {5}.
Therefore, (AB)~(AC) = {5}.