Question

Let = {: 2 − 5 + 6 = 0}, = {: 0 ≤ < 2}, = {, < 3}. Verify (X( ∪ C) = (X) ∪ (AXC) ​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

{1, 2, 3, 6, 9, 18}

B = {1, 2, 3, 4, 5}

Therefore, A ∪ B = {1, 2, 3, 4, 5, 6, 9, 18}

2. Let A = {0, 1, 2, 3, 4, 5}, B = {2, 4, 6, 8} and C = {1, 3, 5, 7}

Verify (A ∪ B) ∪ C = A ∪ (B ∪ C)

Solution:

(A ∪ B) ∪ C = A ∪ (B ∪ C)

L.H.S. = (A ∪ B) ∪ C

A ∪ B = {0, 1, 2, 3, 4, 5, 6, 8}

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

R.H.S. = A ∪ (B ∪ C)

B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}

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

Therefore, from (1) and (2), we conclude that;

(A ∪ B) ∪ C = A ∪ (B ∪ C) [verified]

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