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>
<em />
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>
<em />
(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>
<em />
<em />