Question

test for the commutative property of union and intersecting of the sets. P={x:x is a real between 2 and 7} Q={x:x is an irrational numbers between 2 and 7}

Answer 1

Answer:

Concept used:

Let A and B be two sets.

The union of A and B is defined as

A∪B = {x/ x∈ A or x∈B }

The intrsection of A and B is defined as

A∩B = {x/ x∈ A and x∈B }

P={x:x is a real numbers between 2 and 7}

Q={x:x is an irrational numbers between 2 and 7}

clearly Q ⊂ P

That is P contains Q

Then

P∪Q = P and Q∪P = P

⇒ P∪Q = Q∪P

Therefore intersection of sets is commutative

since Q ⊂ P, P∩Q = Q and Q∩P = Q

⇒ P∩Q = Q∩P

Therefore intersection of sets is commutative