Chapter 1: Sets

Exercise

Question

Question: 6 (ii)

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Show that for any sets A and B,

(ii) A ∪ (B - A) = (A ∪ B)

Answer

1
Identify the elements represented by B - A.
Venn diagram showing the standard decomposition of two sets into three disjoint regions: A − B, A $\cap$ B, and B − A.
B − A contains elements that belong to B but not to A.
2
Combine set A with the elements of B that are not already in A.
Answer: A $∪$ (B - A) = A $∪$ B
Reason: Adding B − A to set A includes all elements of A together with the remaining elements of B that are not already in A. Thus, the resulting set contains every element of A or B. Therefore, A $∪$ (B − A) = A $∪$ B
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