Chapter 1: Sets

Exercise

Question

Question: 7 (ii)

14 / 17

Using properties of sets, show that

(ii) A ∩ (A ∪ B) = A

Answer

1
Use the Distributive Law of sets to simplify A ∩ (A ∪ B).
Venn diagram showing the standard decomposition of two sets into three disjoint regions: A − B, A $\cap$ B, and B − A.
A $∩$ (A $∪$ B) = (A $∩$ A) $∪$ (A $∩$ B)
2
Use the Idempotent Law of intersection.
(A $∩$ A) $∪$ (A $∩$ B) = A $∪$ (A $∩$ B)
3
Use the Absorption Law.
Answer: A $∪$ (A $∩$ B) = A. Hence, A $∩$ (A $∪$ B) = A
Sponsored320 x 50