Question

2. Test for the commutative property of union and intersection of the sets P= { r: x is a real number between 2 and 7} and Q = { x: v is a rational number between 2 and 7).​

Answer 1

Step-by-step explanation:

Commutative Property of union of sets  (A ∪ B)’ = (B ∪ A)  Here P = {3, 4, 5, 6}, Q = {√3, √5, √6}  P ∪ Q = {3, 4, 5, 6} ∪ {√3, √5, √6}  = {3, 4, 5, 6, √3, √5, √6} ... (1)  Q ∪ P = {√3, √5, √6} ∪ {3, 4, 5, 6} = {√3, √5, √6, 3, 4, 5, 6} … (2)  (1) = (2)  ∴ P ∪ Q = Q ∪ P ∴ It is verified that union of sets is commutative.  Commutative Property of intersection of sets  (P ∩ Q) = (Q ∩ P) P ∩ Q = {3, 4, 5, 6} ∩ {√3, √5, √6} = { } … (1)  Q ∩ P = {√3, √5, √6} ∩ {3, 4, 5, 6} = { } … (2) From (1) and (2)  P ∩ Q = Q ∩ P  ∴ It is verified that intersection of sets is commutative.