Answer:
The complement of a set A, denoted A', is the set of all elements that are not in A. The complement of B, denoted B', is the set of all elements that are not in B.
Explanation:
(a) A' = {b, d}
(b) B' = {a, c, d}
(c) A' U B = {a, b, c, d, e} (the union of A' and B contains all elements in both sets)
(d) A U B' = {a, b, c, e} (the union of A and B' contains all elements in both sets)
(e) A' n B = {} (the intersection of A' and B is an empty set)
(f) A n B' = {c} (the intersection of A and B' contains all elements that are in A but not in B)
(g) A' U A = {a, b, c, d, e} (the union of A' and A is the universal set, containing all elements)
(h) B' n B = {} (the intersection of B' and B is an empty set)
(i) A U B = {a, b, c, e} (the union of A and B contains all elements in both sets)
(j) A' U B' = {a, b, c, d, e} (the union of A' and B' is the universal set, containing all elements)
(k) [A n B]' = {b, d} (the complement of the intersection of A and B is the union of the complements of A and B)
(l) A' n B' = {} (the intersection of A' and B' is an empty set).
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