# Thread: Struggling to understand logic tables and proposition

1. ## Struggling to understand logic tables and proposition

So another topic in which I have failed to get a grasp of so here I am coming to a forum for help

Basically for the last 3 weeks or so we have been learning about logic tables and stuff. I kinda understand it when I read it, but putting them into a table, or making a formular for a table I just dont get it.

It says the assignment is

You are given a 4-variable propositional logic function in the form of a truth-table generated by MATLAB code. The assignment tasks are: to obtain the disjunctive normal form (using tutorial instructions given later in this document); to simplify the disjunctive normal form using algebraic identities to implement the full and simplified forms in MATLAB code and finally to verify that the simplified logic functions give the same truth-table as that
originally obtained from the supplied code.

But this makes absolutely no sense to me... and my lecturer is too busy to spend one to one time with me

2. ## Re: Struggling to understand logic tables and proposition

Concerning your second remark in red, "where s came from," it's probably a typo at this point. I would not worry about this.

The third remark in red is about an example of simplifying a DNF. It's not necessary to replace p /\ q by s; you can just replace back s with p /\ q in every line there. The point is that one can replace a part of an expression that matches the left-hand side of an equivalence like p /\ (q \/ r) <-> (p /\ q) \/ (p /\ r) with the right-hand side (or vice versa). The intention is a serious of rewrites is to make the original DNF expression simpler.

3. ## Re: Struggling to understand logic tables and proposition

I think you just need a more intuitive way to explain what they're doing. First, you want to look for any set of truth values that show up within multiple parentheses. Replace those with a single truth value - so in that case they chose s to represent p ^ q. In a more complicated expression, you could replace more pairs or triples with symbols. It just makes the algebra easier.

Second, use basic truth laws to simplify the expression. This just takes practice. From the first to the second line, you see (s^~r) v (s^r) --> s^(~r v r) because of distributive properties. You then notice that if you have either r of ~r, it really doesn't matter what r is - so get rid of it (the T in the third lines says that r v ~r is true no matter what, so leave it out, since we only care about truth variables that can change). The fourth line is, once again, using those distributive laws.

4. ## Re: Struggling to understand logic tables and proposition

Originally Posted by jsndacruz
I think you just need a more intuitive way to explain what they're doing. First, you want to look for any set of truth values that show up within multiple parentheses. Replace those with a single truth value
The words "truth value" should be replaced by "propositional variable." A truth value is T or F; variables are p, q, etc. Interpretations are functions that map variables to truth values.