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Let A fa, b,c. B [a, b, d), and C tb, d,e. Find the union of A and B, and then the union of this with C. Also, find the union of the B and C and then the union of this with A. Try to formulate what you have observed.

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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}

Step-by-step explanation:

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}          because we do not need to list a & b twice

(A ∪ B) ∪ C = {(A ∪ B) & C)

                  = {a, b, c, d & b, d, e}

                  = {a, b, c, d, e}     because we do not need to list b & d twice

B ∪ C = {A & B}

         = {a, b, d & b, d, e}

         = {a, b, d, e}           because we do not need to list b & d twice

(B ∪ C) ∪ A = {(B ∪ C) & A)

                  = {a, b, d, e & a, b, c}

                  = {a, b, c, d, e}     because we do not need to list a & b twice

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