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Given a = {0, 1, 2, 4, 5}, B = {0, 2, 4, 6, 8} and C = {0, 3, 6, 9}. Show that a ∪ (B ∪ C) = (A ∪ B) ∪ C I.E. the Union of Sets is Associative. - Mathematics

Sum

Given A = {0, 1, 2, 4, 5}, B = {0, 2, 4, 6, 8} and C = {0, 3, 6, 9}. Show that  A ∪ (B ∪ C) = (A ∪ B) ∪ C i.e. the union of sets is associative.

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Solution

A = {0, 1, 2, 4, 5}
B = {0, 2, 4, 6, 8}
C = {0, 3, 6, 9}

B ∪ C = {0, 2, 4, 6, 8} ∪ {0, 3, 6, 9}

= {0, 2, 3, 4, 6, 8, 9}

∴ A ∪ (B ∪ C)

= {0, 1, 2, 4, 5} ∪ {0, 2, 3, 4, 6, 8, 9}

⇒ A ∪ (B ∪ C)

= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}    ......(i)

A ∪ B = {0, 1, 2, 4, 5} ∪ {0, 2, 4, 6, 8}

= {0, 1, 2, 4, 5, 6, 8}

∴ (A ∪ B) ∪ C

= {0, 1, 2, 4, 5, 6, 7, 8} ∪ {0, 3, 6, 9}

⇒ (A ∪ B) ∪ C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}  ...II

From I and II, we get

A ∪ (B ∪ C) = (A ∪ B) ∪ C

Concept: Distributive Laws
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Selina Concise Mathematics Class 8 ICSE
Chapter 6 Sets
Exercise 6 (D) | Q 4.1 | Page 72
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