6. Five mark exercise problems I

Test for the commutative property of union and intersection of the sets

 

\(P = \{x: x \ \text{is a real number between} \ 2 \ \text{and} \ 7\}\) and \(Q = \{x: x \ \text{is a rational number between} \ 2 \ \text{and} \ 7\}\).

 

Answer:

 

\(P =\)  and \(Q =\)

 

(i) Commutative property of union of sets:

 

\(P \cup Q =\)  ---- (\(1\))

 

\(Q \cup P =\)  ---- (\(2\))

 

From (\(1\)) and (\(2\)), \(P \cup Q = Q \cup P\)

 

Hence, we proved.

 

(ii) Commutative property of intersection of sets:

 

\(P \cap Q =\)  ---- (\(3\))

 

\(Q \cap P =\)  ---- (\(4\))

 

From (\(3\)) and (\(4\)), \(P \cap Q = Q \cap P\)

 

Hence, we proved.