# Thread: Logic garhh!! need some help

1. ## Logic garhh!! need some help

I'm learning logic and I have to prove algebraically that:

the AND operator may be expressed in terms of the
NOR operator as follows: p AND q= (p NOR p) NOR (q NOR q)

I have no idea how to work this out because I don't understand the second part. I understand p AND p perfectly well but how do I work this out using algebra?

I used the words as I was having problems with the copy and pasting the symbols.

Can you show me each step involved in breaking this down and working it out please I really need some help

**EDIT**

I have a screenshot here from a website I was refered to the other day and it proves it but doesn't show the working out... this is what I need to learn.

2. ## Re: Logic garhh!! need some help

Logical NOR - Wikipedia, the free encyclopedia
"The NOR operation is a logical operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false. In other words, it produces a value of false if and only if at least one operand is true."

When is the right side true? When both p NOR p and q NOR q are false; that is, when both p and q are true.

For a visual explanation, see the Venn diagrams on the Wikipedia page above.

Edit- Using sets:
The intersection of p and q can be expressed as the complement of the union of the complement of p and the complement of q.

3. ## Re: Logic garhh!! need some help

Thanks but you haven;t really shown any working out so it doesn't help me much

4. ## Re: Logic garhh!! need some help

Originally Posted by uperkurk
be expressed in terms of the
NOR operator as follows: p AND q= (p NOR p) NOR (q NOR q).
Note that $\displaystyle \neg \left( {p \vee p} \right) \equiv \neg p$.
Likewise $\displaystyle \neg \left( {q \vee q} \right) \equiv \neg q$.
Then you have $\displaystyle \neg \left( {\neg p \vee \neg q} \right) \equiv p \wedge q$

5. ## Re: Logic garhh!! need some help

That you so much Plato. Can you tell me which laws you used?

6. ## Re: Logic garhh!! need some help

Originally Posted by uperkurk
Can you tell me which laws you used?
This is not a tutorial service. So you need to learn the basic rules in the text material.
You should have a set of basic rules.
For example: $\displaystyle \neg \left( {p \vee q} \right) \equiv \neg p \wedge \neg q$.

7. ## Re: Logic garhh!! need some help

So what you wrote their is perfectly acceptable and simplified enough for full marks?