Question

Using properties of sets, show that: $A \cap (A \cup B)= A$

Answer 1

LHS = A ∩ (A ∪ B) 

Use distribution property,

e.g., $P\cap(Q\cup R)=(P\cap Q)\cup(P\cap R)$

= (A ∩ A) ∪ (A ∩ B) 

Use relation A ∩ A = A 

= (A ∩ A) ∪ (A ∩ B) 

= A ∪ (A ∩ B) 

= A = RHS 

Hence, A ∩ (A ∪ B) = A