# Converse and Contrapositive

• Oct 30th 2009, 02:51 AM
telinos
Converse and Contrapositive
Hello everyone!

i am strungling here doing my excersise actually, lets see now, i have this expression : A positive integer is a prime number only if it doesnt have divisor past 1 and itself.

Converse is : If an integer doesnt have divisor past 1 and itself then its a positive integer prime number.

Cotrapositive is : A positive integer is not a prime number only if it does have divisor past 1 and itself .

Am i right? any suggestions?

By the way i might have translated bad the definition of prime numbers from my native language into english, so please excuse me.

• Oct 30th 2009, 03:13 AM
Plato
Quote:

Originally Posted by telinos
I am strungling here doing my excersise actually, lets see now, i have this expression : A positive integer is a prime number only if it doesnt have divisor past 1 and itself.

Converse is : If an integer doesnt have divisor past 1 and itself then its a positive integer prime number.

Cotrapositive is : A positive integer is not a prime number only if it does have divisor past 1 and itself .

First write the statement is the 'If - then' form.
If A positive integer is a prime number then it doesn't have divisor past 1 and itself.

Now the converse: If A positive integer doesn't have divisor past 1 and itself then it is a prime number .

You do the contrapositive.
• Oct 30th 2009, 06:58 AM
telinos
Quote:

Originally Posted by Plato
First write the statement is the 'If - then' form.
If A positive integer is a prime number then it doesn't have divisor past 1 and itself.

Now the converse: If A positive integer doesn't have divisor past 1 and itself then it is a prime number .

You do the contrapositive.

Okay thanks for your response, so the 1st i had to do, is to write the given statement in the "IF - then " form right ?

So the Contrapositive is : If a positive integer does have divisor past 1 and itself then it is not a prime number.

Is that right?

So the Contrapositive of the 1st given statement is actually true statement.

The Converse is also a true statement. Shouldnt it be false according to the theory?

Looking forward for your confirmation !
• Oct 30th 2009, 07:41 AM
Plato
Quote:

Originally Posted by telinos
Okay thanks for your response, so the 1st i had to do, is to write the given statement in the "IF - then " form right ?

So the Contrapositive is : If a positive integer does have divisor past 1 and itself then it is not a prime number.

Is that right?

So the Contrapositive of the 1st given statement is actually true statement.

The Converse is also a true statement. Shouldnt it be false according to the theory?

Looking forward for your confirmation !

There is one minor change the and should be or.
• Oct 30th 2009, 08:00 AM
telinos
Quote:

Originally Posted by Plato
There is one minor change the and should be or.

Theres a last thing i'd like to know, According to my theory the Converse of a statement should be always false .

On the other hand the converse of the given statement is :

If A positive integer doesn't have divisor past 1 and itself then it is a prime number .

So my question is: The new definition that comes out from the converse seems true, shouldnt it be false according to theory? is that an exception?
• Oct 30th 2009, 08:18 AM
Plato
Quote:

Originally Posted by telinos
Theres a last thing i'd like to know, According to my theory the Converse of a statement should be always false .

I hope that you were not taught that nor did any textbook say that.
It is completely wrong.

Consider:
If a rhombus contains a right angle then it is a square.
Converse: If a figure is a square then it is rhombus containing a right angle.
Both of those statements are true.

It is true the implication and its contrapositive have the same truth value.
The converse and inverse have the same truth value.
• Oct 30th 2009, 09:17 AM
telinos
Quote:

Originally Posted by Plato
I hope that you were not taught that nor did any textbook say that.
It is completely wrong.

Consider:
If a rhombus contains a right angle then it is a square.
Converse: If a figure is a square then it is rhombus containing a right angle.
Both of those statements are true.

It is true the implication and its contrapositive have the same truth value.
The converse and inverse have the same truth value.

Oh yeah indeed, actually i meant that if for example, we have this statement p --> q , the converse statement of this is, q --> p ,
and p --> q not equivalent q --> p , thats what my theory actualy
says, so i think all right .
Thanks again