Tamil Nadu Board of Secondary EducationHSC Science Class 11

By taking suitable sets A, B, C, verify the following results: (B − A) ∪ C = (B ∪ C) − (A − C) - Mathematics

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Sum

By taking suitable sets A, B, C, verify the following results:

(B − A) ∪ C = (B ∪ C) − (A − C)

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Solution

To prove the following results let us take U = {1, 2, 5, 7, 8, 9, 10}

A = {1, 2, 5, 7}

B = {2, 7, 8, 9}

C = {1, 5, 8, 7}

Let A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8}

B – A = {3, 4, 5, 6} – {1, 2, 3, 4}

B – A = {5, 6}

(B – A) ∪ C = {5, 6} ∪ {5, 6, 7, 8}

(B – A) ∪ C = {5, 6, 7, 8}   ......(1)

B ∪ C = {3, 4, 5, 6} ∪ {5, 6, 7,8}

B ∪ C = {3, 4, 5, 6, 7, 8}

A – C = {1, 2, 3, 4} – {5, 6, 7, 8}

A – C = {1, 2, 3 , 4}

(B ∪ C) – (A – C) = {3, 4, 5, 6, 7, 8} – {1, 2, 3, 4}

(B ∪ C) – (A – C) = {5, 6, 7, 8}  ......(2)

From equations (1) and (2)

(B – A) ∪ C = (B ∪ C) – (A – C)

Concept: Sets
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Chapter 1: Sets, Relations and Functions - Exercise 1.1 [Page 7]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 1 Sets, Relations and Functions
Exercise 1.1 | Q 4. (vi) | Page 7
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