Question

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.

Answer 1

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}

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