Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th
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If A = {x : x ∈ Z, −2 < x ≤ 4}, B = {x : x ∈ W, x ≤ 5}, C = {− 4, −1, 0, 2, 3, 4} verify A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) - Mathematics

Sum

If A = {x : x ∈ Z, −2 < x ≤ 4}, B = {x : x ∈ W, x ≤ 5}, C = {− 4, −1, 0, 2, 3, 4} verify A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

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Solution

A = {x : x ∈ Z, −2 < x ≤ 4} = {−1, 0, 1, 2, 3, 4}

B = {x : x ∈ W, x ≤ 5} = {0, 1, 2, 3, 4, 5}

C = {−4, −1, 0, 2, 3, 4}

A ∪ (B ∩ C)

B ∩ C = {0, 1, 2, 3, 4, 5} ∩ {−4, −1, 0, 2, 3, 4}

= {0, 2, 3, 4}

A ∪ (B ∩ C) = {−1, 0, 1, 2, 3, 4} ∪ (0, 2, 3, 4}

= {−1, 0, 1, 2, 3, 4}  ...(1)

(A ∪ B) ∩ (A ∪ C)

A ∩ B = {0, 1, 2, 3, 4}

A ∩ C = {−1, 0, 2, 3, 4}

(A ∩ B) ∪ (A ∩ C) = {0, 1, 2, 3, 4} ∪ {−1, 0, 2, 3, 4}

= {−1, 0, 1, 2, 3, 4}   ...(2)

From (1) and (2), it is verified that

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

  Is there an error in this question or solution?
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Samacheer Kalvi Mathematics Class 9th Tamil Nadu State Board
Chapter 1 Set Language
Exercise 1.5 | Q 3 | Page 28
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