Exercices

Wednesday, 20 February 2019

10:35 AM

• Prove that if  and , then

Proof (actually write this down)

Suppose that  and  and that

Then  or

 

If , then  because

If , then  because

 

Which proves that

In both cases,  which proves that

 

 

 

• Prove that if  and  then

Proof: Suppose that  and  then

Let

Then  since

Similarly,  since

Hence

Thus

 

• Prove that if  then

Proof: Suppose that

By definition,

 

Let , since  it follows that

Then , so

Hence,

 

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