Boolean Logic and Truth Tables help?

[s1l3nced]

Hey all. I am enrolled in a computer programming course. One of my classes, I have to construct a truth table for the following expressions:

a XOR NOT(a) AND NOT(b)

NOT((a OR NOT(b)) AND (NOT(a) OR c) AND (b OR c)
or
~((aV~b)&(~aVc)&(bVc))

Actually I tried completing the second expression and here's my truth table. I'm comparing it to online truth table generators but I can't seem to understand one part. I'll explain after I type it out.

a b c  ~((aV~b)&(~aVc)&(bVc))
T T T F 
T T F T
T F T F
T F F T
F T T 
F T F T
F F T F
F F F T

I've left the 5th down and 5th over piece blank because all over the internet it says T. However, I can't help but to disagree.

Step 1:
~a [OR] ~~b (is b) is TRUE (~a is true in table)
~~a (is a) [OR] ~c is FALSE (a is false, and c is true in table)
~b or ~c is FALSE (both are true in the table)

Online though, on the generators, they say it's true. How can it be true? I thought at least one of each variable in paranthesis has to be true? Right off the bat.. ~(bVc) cannot be true is b and c are true in the table, which they are in mine.

I know I'm asking for a lot, but I hope someone here is generous enough to help!

Edit: If you can help me with my homework, I am willing to pay you. Not specifying an amount on here, but we can talk in private if interested.

 

[thephoenix25]

As far as I can see in line 5 :

a = F
b = T
c = T

NOT((a OR NOT(b)) AND (NOT(a) OR c) AND (b OR c))


(a OR NOT(b)) = (F OR NOT(T)) = (F OR F) = F

(NOT(a) OR c) = (NOT(F) OR T) = (T OR T) = T

(b OR c) = (T OR T) = T

(F) AND (T) AND (T) = F

NOT(F) = T

So by my understanding the result will be T.

's been a while since I last did this kind of stuff so don't take my word for it. But I think you may not have noticed that the NOT statement at the start inverts whatever result you end up with.

These are worked out first

(a OR NOT(b)) AND (NOT(a) OR c) AND (b OR c)

Then the result is inverted by the leading NOT

Hope this helps, but please check it through yourself as I don't wanna mess with your education.

 

[s1l3nced]

As far as I can see in line 5 :

a = F
b = T
c = T

NOT((a OR NOT(b)) AND (NOT(a) OR c) AND (b OR c))


(a OR NOT(b)) = (F OR NOT(T)) = (F OR F) = F

(NOT(a) OR c) = (NOT(F) OR T) = (T OR T) = T

(b OR c) = (T OR T) = T

(F) AND (T) AND (T) = F

NOT(F) = T

So by my understanding the result will be T.

's been a while since I last did this kind of stuff so don't take my word for it. But I think you may not have noticed that the NOT statement at the start inverts whatever result you end up with.

These are worked out first

(a OR NOT(b)) AND (NOT(a) OR c) AND (b OR c)

Then the result is inverted by the leading NOT

Hope this helps, but please check it through yourself as I don't wanna mess with your education.

Awesome work. I really appreciate the coloring system you used to help me scan it easier.

I have a question, though. Say it was.. T OR F. Could that be interpreted as T? Using OR means either one has to be true.. So...

a b aVb
T T T
T F T
F T T
F F F

Just to clarify. Thank you very much for replying by the way. How do you have experience with programming? Is that what you do as a career?

 

[thephoenix25]

Awesome work. I really appreciate the coloring system you used to help me scan it easier.

I have a question, though. Say it was.. T OR F. Could that be interpreted as T? Using OR means either one has to be true.. So...

a b aVb
T T T
T F T
F T T
F F F

Just to clarify. Thank you very much for replying by the way. How do you have experience with programming? Is that what you do as a career?

Hi,

Yes, your truth table for aVb is correct.

T OR T = T
T OR F = T
F OR T = T
F OR F = F

OR = if one side is true

If either side of an "OR" statement is true then the result will always be true.

T AND T = T
T AND F = F
F AND T = F
F AND F = F

AND = if both sides are true

For an "AND" statement, both sides of the statement must be true to get a true result.

hope this helps

 

[thephoenix25]

Post removed 'cos it was incorrect