Propositional Logic Symposia - [2] – Truth Funct. Logic, Truth Tables, Conjunctions

[kennethamy]

Originally Posted by VideCorSpoon

Yeah, I never really thought about it like that! The truth table is basically an account of what the different combinations of truth values would be for a given argument. I guess a comparison could be made between the dual truth values and the punnett square alleles. But the dominant and recessive traits of truth values comes only from the inference rules.

It can also be put as follows:

1. T v X = T
2. F v X = X
3. T & X = X
4, F & X = F
5. T > X = X
6. F > X = T
7. X > T = T
8. X > F = X

[VideCorSpoon]

Thats an interesting way of putting it.

From what I gather, x is a function of (T or F) wherein any variability of those two values equal true, because a disjunction is false only when both disjuncts are false. So I would think that #2's usage of the x is problematic as the x in the right disjunct could be have two separate overall values.

I think the same can be said for the conjunction and the conditionals.

[kennethamy]

Originally Posted by VideCorSpoon

Thats an interesting way of putting it.

From what I gather, x is a function of (T or F) wherein any variability of those two values equal true, because a disjunction is false only when both disjuncts are false. So I would think that #2's usage of the x is problematic as the x in the right disjunct could be have two separate overall values.

I think the same can be said for the conjunction and the conditionals.

1. T v X = T
2. F v X = X
3. T & X = X
4, F & X = F
5. T > X = X
6. F > X = T
7. X > T = T
8. X > F = X

But if (in 2) X is F, then the whole expression is F. And if X is T, then the whole expression is T. So 2= whatever X is.

[VideCorSpoon]

That seems problematic because, if we use #2 as an example (i.e. F v X = X) the X (last x in the line) to a point needs to be defined as either true or false. It kinda cuts down on excess logic. Its correct.

I get where you are coming from. Lines 1 makes sense. Because line 1 has a true value, whatever the value of the next variable, the result will always be true because a disjunction can only be false when both disjuncts are false. But it gets confusing when you approach line 2. Since there is a false in the left disjunct, you run into 2 possibilities of it being either true or false. So I think the problem lies in the dual use of x in such a defined system.

It is right, but it seems more complicated than it should be. My argument is based more on basic understandability. But still, good stuff.

[Jimmy53]

Could anyone please explain how to get the answer for the following Truth Table. Unfortunately, I'm new to these and just can not quite understand them yet.


Q:
In relation to TRUTH TABLES, if A has the value TRUE and B has the value FALSE, what would f have if f = A AND B?

[Arjen]

Originally Posted by Jimmy53

Could anyone please explain how to get the answer for the following Truth Table. Unfortunately, I'm new to these and just can not quite understand them yet.


Q:
In relation to TRUTH TABLES, if A has the value TRUE and B has the value FALSE, what would f have if f = A AND B?

FALSE. It would only have true if both A AND B would have the truth value TRUE; hence the name.

[Jimmy53]

Hi Arjen

Thanks very much for your reply, much appreciated. I have only started to try truth tables and just can seem to grasp them. Hopefully I think I've got it now.

Many thanks again for your speedy reply.
Jim

[Arjen]

The speed was due to luck Jimmy. If you have more questions, perhaps I can be of further assistance. If not I bet VideCorSpoon can be...or perhaps him and me together...or something..



Is your interest a private matter, or one stimulated by school by the way?

[VideCorSpoon]

The main thing to remember about truth tables is the fact that a table will show you the possible truth combinations for a certain argument. When you stated that the assigned truth values of A=T and B=F, you must mean that on a specific line of your truth table. Remember the truth possibility matrix will give you the different combinations. The lower case f I am assuming is the transference of the truth probability matrix value. The lower case f (if I understand your question right) will always be false. The litmus test comes when you have to apply the rules (conjunction, disjunction, etc.) to the truth tables.

[Alanocrates]

Spoon, I am still not solid on understanding the "matrix" thing. Is this important to know for future logic things.

BTW, I just started college a day ago and logic is a class a have to take. It seems very intimidating to me becuse I am no good in math. Do you think this will effect my ability to get logic down????? It seems very scary to me. Do you think I should take math courses to prepare myself for this class????

also, thnx for the tutorials.

- alan