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सी.आई.एस.सी.ई.आईसीएसई ICSE Class 8

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

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प्रश्न

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.

योग

उत्तर

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, 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, 8} ∪ {0, 3, 6, 9}

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

From (i) and (ii), we get

A ∪ (B ∪ C) = (A ∪ B) ∪ C

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अध्याय 6: Sets - Exercise 6 (D) [पृष्ठ ७२]

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सेलिना Concise Mathematics [English] Class 8 ICSE
अध्याय 6 Sets
Exercise 6 (D) | Q 4.1 | पृष्ठ ७२
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