Proving Logic Statements with Truth Tables and Laws

[wdulli]

Homework Statement

Sometimes i got a question with homework if i can prove something. I got a book where the tolled me to use truthtables to see the outcome :

For example :

(notP V Q) <=> (P => Q)

P Q | notP | notP v Q | P=>Q | (notP V Q) <=> (P => Q)
0 0 | 1 | 1 | 1 | 1
0 1 | 1 | 1 | 1 | 1
1 0 | 0 | 0 | 0 | 1
1 1 | 0 | 1 | 1 | 1

Lateron in the same book it's statement is, that it's easier to use the Logic laws then written down the truthtable everytime. And gives the logic laws for example

1. Double complement
2. The morgan
3. Commutative
4 Associative
etc etc

No my question :

When do i know what to use. Do i allways start with Double complement
, the morgan , Commutative etc.

The Attempt at a Solution

Searched on the internet (Different websites) but i can't find the solution/way. I didnt put the question in this forum post because i want to know the steps to take not the answer.

 

[Filip Larsen]

You can in general use either or both methods (truth tables and algebra rules) as you see fit.

Usually you will want to use truth tables when the number of distinct symbols is low but the number of logical combinations is high (like if you have to evaluate the equivalence of two rather long expressions involving only P and Q). If there is N distinct symbols the truth table has 2^N rows, so for N = 2 or 3 that is really easy.

On the other hand, if you have many symbols, or the expressions are simple, or you can recognize sub-expressions from the list of rules you know, it may be faster or easier to use the rules to prove equivalence.

Of course, you may get an assignment that ask you to use either method to prove something and then you of course have to use that method.