# Propositional logic and Boolean Logic Thread :cool: Tweet

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1. Propositional logic and Boolean Logic Thread :cool:
This for all the users studying logic.
2. Re: Propositional logic and Boolean Logic Thread :cool:
Anyone wanna help me with some truth tables?
3. Re: Propositional logic and Boolean Logic Thread :cool:
My nightmare continues To the student room
4. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)
Anyone wanna help me with some truth tables?
Sure (I'll try )
5. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)
Anyone wanna help me with some truth tables?
go on
6. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by FinalMH)
go on
I don't understand quite well the 3rd and 5th columns.

http://imageshack.us/photo/my-images...1021200243.jpg

Last edited by SoulfulBoy; 21-10-2011 at 20:10.
7. Re: Propositional logic and Boolean Logic Thread :cool:
8. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)
I don't understand quite well the 3rd and 5th columns.

http://imageshack.us/photo/my-images...1021200243.jpg

The third column is:
1. (NOT A and B)
This means when A is FALSE and B is TRUE, then the above statement is TRUE.

The fifth column is:
2. (A and NOT B)
This means when A is TRUE and B is FALSE, then the above statement is TRUE.
9. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by ElMoro)
Sure (I'll try )
[IMG] Uploaded with ImageShack.us[/IMG]
10. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by gff)
The third column is:
1. (NOT A and B)
This means when A is FALSE and B is TRUE, then the above statement is TRUE.

The fifth column is:
2. (A and NOT B)
This means when A is TRUE and B is FALSE, then the above statement is TRUE.

Could you explain the point 1. more explicitly, please? I understand that NOT A is the opposite truth value of A but I don't actually get the third column.
Could you give me examples using actual sentences please?
And the same goes for the point 2.
I guess I am too thick

Cheers, Gff!
11. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)
I don't understand quite well the 3rd and 5th columns.
NOT A AND B (can also be written as or more commonly ) means that it's true when NOT A is true (so A is false) and B is true.

It's similar thing for A AND NOT B. Hope this made sense
12. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)
Could you explain the point 1. more explicitly, please? I understand that NOT A is the opposite truth value of A but I don't actually get the third column.
They will serve me in a shop if I'm not drugged AND I'm over sixteen

Let's say A is me being drugged (so A is true means I am drugged)

And B is me being over sixteen (so if B is true it means I'm over sixteen)

They will serve me if I'm NOT drugged (so NOT A) and over sixteen (which is B)

So for them to serve me NOT A has to be true and B has to be true

If NOT A is true, it means A is false (if I'm not drugged then obviously the statement "I am drugged" is false)

So that means NOT A AND B is true when A is false and B is true

Hope this makes sense
13. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)
I don't understand quite well the 3rd and 5th columns.

http://imageshack.us/photo/my-images...1021200243.jpg

I think they have answered the question

Also if you have some time, this will be extremely helpful if you're stuck.
Last edited by FinalMH; 21-10-2011 at 20:33.
14. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by ElMoro)
They will serve me in a shop if I'm not drugged AND I'm over sixteen

Let's say A is me being drugged (so A is true means I am drugged)

And B is me being over sixteen (so if B is true it means I'm over sixteen)

They will serve me if I'm NOT drugged (so NOT A) and over sixteen (which is B)

So for them to serve me NOT A has to be true and B has to be true

If NOT A is true, it means A is false (if I'm not drugged then obviously the statement "I am drugged" is false)

So that means NOT A AND B is true when A is false and B is true

Hope this makes sense
This was what I needed!!!!!! I see it all clear now!!!
Thank you, so much, sir!

I will give you some pos reps tomorrow (I already spent those I had today )

I will contact you if I have more doubts.
15. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)

Could you explain the point 1. more explicitly, please? I understand that NOT A is the opposite truth value of A but I don't actually get the third column.
Could you give me examples using actual sentences please?
And the same goes for the point 2.
I guess I am too thick

Cheers, Gff!
For the first point.

Example:

I would buy a place on the Moon if they it isn't too expensive, and if I can see it with my telescope.

This can be turned into a propositional logic statement, i.e.

= Places on the Moon are expensive.
= I can see them with my telescope.

Then, the statement = I'll buy a place on the Moon.

This being said, the conditions for to be true are .

This implies that .

Now, you know that I wouldn't buy a place on the moon when is true and is true.
This means that is FALSE when .

What are the other possibilities when I wouldn't buy a place on the moon?
16. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by FinalMH)
I think they have answered the question

Also if you have some time, this will be extremely helpful if you're stuck.
I will watch it, FinalMH.

Thanks!
17. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by gff)
For the first point.

Example:

I would buy a place on the Moon if they it isn't too expensive, and if I can see it with my telescope.

This can be turned into a propositional logic statement, i.e.

= Places on the Moon are expensive.
= I can see them with my telescope.

Then, the statement = I'll buy a place on the Moon.

This being said, the conditions for to be true are .

This implies that .

Now, you know that I wouldn't buy a place on the moon when is true and is true.
This means that is FALSE when .

What are the other possibilities when I wouldn't buy a place on the moon?
You would not buy a place on the moon when:

1. Places on the moon are not expensive and you cannot see them with your telescope.

2. Places on the moon are expensive and you cannot see them with your telescope.

Is it okay?
18. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by gff)
For the first point.

Example:

I would buy a place on the Moon if they it isn't too expensive, and if I can see it with my telescope.

This can be turned into a propositional logic statement, i.e.

= Places on the Moon are expensive.
= I can see them with my telescope.

Then, the statement = I'll buy a place on the Moon.

This being said, the conditions for to be true are .

This implies that .
Not strictly correct. A valid deduction would be . Consider that (strictly speaking) by your original proposition, doesn't imply anything about the truth values of or (only vice versa). Specifically, is vacuously true.
Last edited by Planto; 21-10-2011 at 20:59.
19. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by SoulfulBoy)
You would not buy a place on the moon when:

1. Places on the moon are not expensive and you cannot see them with your telescope.

2. Places on the moon are expensive and you cannot see them with your telescope.

Is it okay?
Yes, it looks okay.
20. Re: Propositional logic and Boolean Logic Thread :cool:
(Original post by ElMoro)
They will serve me in a shop if I'm not drugged AND I'm over sixteen

Let's say A is me being drugged (so A is true means I am drugged)

And B is me being over sixteen (so if B is true it means I'm over sixteen)

They will serve me if I'm NOT drugged (so NOT A) and over sixteen (which is B)

So for them to serve me NOT A has to be true and B has to be true

If NOT A is true, it means A is false (if I'm not drugged then obviously the statement "I am drugged" is false)

So that means NOT A AND B is true when A is false and B is true

Hope this makes sense
[IMG] Uploaded with ImageShack.us[/IMG]

Is the table ok? Also I don't know how to approach A XOR B
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