let U=[a,b,c....z],.A=[a,c,e,f,z,y],..
B=[e,x,y,z],.C=[j,k,l,e,f,y]
find
(i)(AUC)'
(ii) AU(B-A)
To find the answers to these set operations, we need to understand the basic operations involved in set theory.
(i) (A ∪ C)' represents the complement of the union of sets A and C.
To find the complement, we first need to find the union of sets A and C:
A ∪ C = {a, c, e, f, z, y, j, k, l}
To find the complement, we need to take the set of all elements in the universal set U that are not in A ∪ C.
Step 1: List all elements of the universal set U.
U = {a, b, c, ..., z}
Step 2: Identify the elements in A ∪ C.
A ∪ C = {a, c, e, f, z, y, j, k, l}
Step 3: Remove the elements from U that are in A ∪ C.
U - (A ∪ C) = {b, d, g, h, i, m, n, o, p, q, r, s, t, u, v, w, x}
So, (A ∪ C)' = {b, d, g, h, i, m, n, o, p, q, r, s, t, u, v, w, x}
(ii) A ∪ (B - A) represents the union of A and the difference between B and A.
To find the difference between B and A, we need to remove the elements that are common to both sets B and A.
Step 1: List all elements of set B.
B = {e, x, y, z}
Step 2: Identify the elements in set A that are also in set B.
Common elements in A and B: {e, z, y}
Step 3: Remove the common elements from B.
B - A = {x}
Step 4: Find the union of A and (B - A).
A ∪ (B - A) = {a, c, e, f, z, y, x}
So, A ∪ (B - A) = {a, c, e, f, z, y, x}
Please note that the answers might vary based on the given sets A, B, C, and the universal set U.