# Predicates Help

• Mar 4th 2009, 10:31 AM
M.A.T.H
Predicates Help
We have the predicates E and O describing integers, defined by E(n) is true if n is even, and O(n) is true if n is odd.

(a) Express in predicate calculus notation the sentence the sum of two odd integers is even.

(b) Give the negation of the predicate http://img3.imageshack.us/img3/9336/matho.jpg

Thank You

Sorry if this is in the wrong section im new here
• Mar 4th 2009, 11:28 AM
Plato
Quote:

Originally Posted by M.A.T.H
We have the predicates E and O describing integers, defined by E(n) is true if n is even, and O(n) is true if n is odd.
(a) Express in predicate calculus notation the sentence the sum of two odd integers is even.
(b) Give the negation of the predicate http://img3.imageshack.us/img3/9336/matho.jpg
Thank You
Sorry if this is in the wrong section im new here

Welcome to the forum.
This is indeed the correct forum for your question.
However, we want you to show some effort on your part.
At least tell us what you do not understand about the question.

Just posting the question and then waiting for an answer is not the way it works.
• Mar 4th 2009, 12:28 PM
M.A.T.H
Quote:

Originally Posted by M.A.T.H
We have the predicates E and O describing integers, defined by E(n) is true if n is even, and O(n) is true if n is odd.

(a) Express in predicate calculus notation the sentence the sum of two odd integers is even.

(b) Give the negation of the predicate http://img3.imageshack.us/img3/9336/matho.jpg

Thank You

Sorry if this is in the wrong section im new here

Well i dont get what 6a is asking or how to do it, im not asking for the answers just how it would be done?

And for 6b i had a go but not sure show below (as im new here im not sure how to get all them symbols etc so gna have to type it up)

Backwords E = E
Z with extra line in it = Z
Upside down A = A

Em is an element of Z|O(2m) = Am is an element of Z such that ¬O(2m)
• Mar 4th 2009, 12:52 PM
Plato
For part a): $\left( {\forall x} \right)\left( {\forall y} \right)\left[ {O(x) \wedge O(y)\, \Rightarrow \,E(x + y)} \right]$

You made a good start on part b): $\left( {\forall x} \right)\left[ {\neg O(2x)} \right]$.

For negations in general use these two rules.
$\neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]\;\& \,\neg \left( {\exists x} \right)\left[ {P(x)} \right] \equiv \left( {\forall x} \right)\left[ {\neg P(x)} \right]$
• Mar 4th 2009, 02:27 PM
M.A.T.H
Hey check your pm please :) thank you, also how to you know what terms u have to put in to get the upside down A and also how can u edit previous posts i cant seem to find the edit button... (could only find it on this post now)
• Mar 4th 2009, 02:37 PM
Plato
Quote:

Originally Posted by M.A.T.H

Sorry, but that is not the way I choose to work!
You post your question here so all can profit from them.
• Mar 4th 2009, 02:50 PM
M.A.T.H
Quote:

Originally Posted by Plato
Sorry, but that is not the way I choose to work!
You post your question here so all can profit from them.

Ahh ok no problem one second let me just copy paste it from my sentbox lol..

Quote:

Originally Posted by M.A.T.H
Hey i would just like to thank you for your help, i tried to work the question out myself and this is what i got its a little different from yours can you help me with what iv done wrong:

Quote:

Originally Posted by Plato
For part a): $\left( {\forall x} \right)\left( {\forall y} \right)\left[ {O(x) \wedge O(y)\, \Rightarrow \,E(x + y)} \right]$

You made a good start on part b): $\left( {\forall x} \right)\left[ {\neg O(2x)} \right]$.

For negations in general use these two rules.
$\neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]\;\& \,\neg \left( {\exists x} \right)\left[ {P(x)} \right] \equiv \left( {\forall x} \right)\left[ {\neg P(x)} \right]$

Above is yours this is what u got:

a)
${\forall n}$ is and element of Z|O(2n) $\wedge$ E(n)

b)
${\forall m}$ is an element Z|O(2m) => E(m)

Can you tell me what or where im going wrong...Please

I cant seem to do 6b properly..I have to express the result back in english, and wernt sure how to express your answer...So could u help with that please?

Thank you
• Mar 4th 2009, 03:18 PM
Plato
Frankly I don’t know what to say about you are doing.
Below is the correct answer for part a) [I did add to clarify domain].
a): $\left( {\forall x \in \mathbb{Z}} \right)\left( {\forall y \in \mathbb{Z}} \right)\left[ {O(x) \wedge O(y)\, \Rightarrow \,E(x + y)} \right]$

You can do the same thing for part b).
The ‘English’ translation of the negation is:
“No integer is such that twice the integer is odd.”
Or “Two times any integer is not odd.”