Question

How can I express p^q(p and q) in terms of NAND operator... my professor says its (p!p)!(q!q) but i think thats wrong after I made my truth table....

Also pvq

Answer 1

p ! p (meaning p NAND p) has input:
1) 0 0 0 ! 0 = not( 0 ^ 0) = not(0) = 1
2) 1 1 1 ! 1 = not(1 ^ 1) = not(1) =0
so it negates the input (equivalent to NOT(p) )

last 2 columns NOT(and)= NAND
p q NOT(p) NOT(q) and NOT
0 0 1 1 1 0
0 1 1 0 0 1
1 0 0 1 0 1
1 1 0 0 0 1

so that looks like OR

Answer 2

one way to get AND is (p!q)!1

Answer 3

we use T and F. Im assuming 0 is false and 1 is true? Here is my truth table for the p^q

Answer 4

so idk how he got (p!p)!(q!q)

Answer 5

As I posted above (p!p)!(q!q) is p OR q

to get AND, notice that if you negate p!q you get AND


so you could do (p!q)!(p!q)
that is using the idea that NOT(p)= p!p . in this case we are doing NOT(p!q)

Answer 6

ok and your not column is for !(p^q)?

Answer 7

just to be clear, what symbol are you using for NAND ?

I get ^ = AND
v = OR
? = NAND
? = NOT
what are your symbols for NAND and NOT ?

Answer 8

my professor can't seem to make up his mind but:

Not = ~
NAND = !
And = ^
Or = v

Answer 9

In that case
a ! b = a NAND b = NOT(a AND b) = ~(a ^ b)
notice that (p!p)!(q!q) = ~ ( (p!p) ^ (q!q) ) = ~( ~p ^ ~q)

my last column is
~ ( ~p ^ ~q)
which if you know boolean algebra, equals p v q

Answer 10

ok I understand that but in my p ^ q column, I have T,F,F,T. When i evaluate (P!P)!(q!q) I get T,T, T, F so it seems they arent equal idk what im evaluating wrong

Answer 11

Your table does not seem correct
p q p^q p!q p!p q!q
T T T F F F
T F F T F T
F T F T T F
F F F T T T

the entries are correct. but what are you calculating ?
if you are doing (p!p) ! (q!q)
then you should have p q as the first two columns (which you do)
then you should do p!p and q!q (because those values will go into
(p!p) ! (q!q)

Answer 12

Notice how I did p q then p!p q!q (which are the same as ~p and ~q)
then p!p ^ q!q (same as ~p ^ ~q)
and finally
~(p!p ^ q!q) which is the same as (p!p) ! (q!q)

Answer 13

Yes that is what I am doing. I see that I have both (p!p) and (q!q) in my table. So I plug the truth values into (p!p)!(q!q). For the first one for example, F!F = Not(False and False) = T

Answer 14

but why do you have the column p ^ q ?

Answer 15

I made the column p ^ q so that I have the truth values there to compare to (p!p)!(q!q) to see if they are equal

Answer 16

ok. and why do you have p!q ?

Answer 17

I made it because I thought my professor's answer was wrong so I was trying different things but I guess its redundant

Answer 18

I have all the correct values in my table but the truth values of p^q and (p!p)!(q!q) aren't matching up for me idk why

Answer 19

they won't.

First, take out the column p!q
then at the right side add the column (~p) ! (~q)
which is the same as (p!p)!(q!q)
you will get my table, and the last column will be the same as p v q
which is your second question.

(you might want to replace the 3rd column p^q with p v q so you can compare them)

Answer 20

to get AND, notice that if you negate p!q you get AND


try (p!q)!(p!q)

Answer 21

Wait we were doing And first correct?

Answer 22

why would I replace p^q with pvq?

Answer 23

because your expression (p!p)!(q!q) is the same as p v q

so you are answering your second question *** Also pvq ***

Answer 24

so when my professor says that p^q = (p!p)!(q!q) how is that true if their values dont match? what makes it true?

Answer 25

either he or you made a mistake.

Answer 26

so the Truth values should match then correct?

Answer 27

Yes, the truth values have to come out the same if the expressions mean the same thing.

Answer 28

Ah ok. So I notice that (p!p)!(q!q) = pvq(p OR q). In class, my professor must have made a mistake by telling us AND. Is that correct?

Answer 29

something got lost in the translation.... but I cannot say if it was him or you. However, in class you can ask him.

Answer 30

Ok one last question. Since I have or...Would would be an expression = for p^q

Answer 31

when people say "mind your p's and q's" (meaning be careful) they say that because it is easy to mix up the p's and q's

an expression of p ^ q using NANDS is (p!q) ! (p!q)
which looks almost the same as (p!p)!(q!q) if you are dyslexic


***
Ok one last question. Since I have or...Would would be an expression = for p^q
***
I don't understand the question.

Answer 32

OK, now I understand. You are asking what's an expression using NANDs for p ^ q

see above post.

Answer 33

correct

Answer 34

Thank you so much for your help. I think I did get p's and q's mixed up somehow Lol