Chapter 1: Sets

Exercise

Question

Question: 7 (i)

13 / 17

Using properties of sets, show that

(i) 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 union.
(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