Answer: A ∪ B = {a, b, c, d}
(A ∪ B) ∪ C = = {a, b, c, d, e}
B ∪ C = = {a, b, d, e}
(B ∪ C) ∪ A = = {a, b, c, d, e}
<u>Step-by-step explanation:</u>
A = {a, b, c} B = {a, b, d} C = {b, d, e}
Union means "to join" so combine the sets to form a union.
A ∪ B = {A & B}
= {a, b, c & a, b, d}
= {a, b, c, d} <em>because we do not need to list a & b twice</em>
(A ∪ B) ∪ C = {(A ∪ B) & C)
= {a, b, c, d & b, d, e}
= {a, b, c, d, e} <em>because we do not need to list b & d twice</em>
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B ∪ C = {A & B}
= {a, b, d & b, d, e}
= {a, b, d, e} <em>because we do not need to list b & d twice</em>
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(B ∪ C) ∪ A = {(B ∪ C) & A)
= {a, b, d, e & a, b, c}
= {a, b, c, d, e} <em>because we do not need to list a & b twice</em>
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