Thread: Using truth tables to show logical consistancy between logical expressions

How do you set up a truth table to show that these expressions are consistant:

p -> q
q -> r
r -> p
-q

I'm basically asking how to solve question 51 of the first exercise in the book "Discreet Mathematics And Its Applications".

I've already solved the problem but I'd like to know how to use a truth table to solve it.

Originally Posted by smkxn

How do you set up a truth table to show that these expressions are consistant:

p -> q
q -> r
r -> p
-q

I'm basically asking how to solve question 51 of the first exercise in the book "Discreet Mathematics And Its Applications".

I've already solved the problem but I'd like to know how to use a truth table to solve it.

1) I have the book (6-th edition) and I can't find this exercise. Where exactly is it? Please write down chapter, section , number , etc.

2) What exactly does the exercise ask? The different lines you wrote are obviously not logically equivalent since there appear different letters in them: perhaps you want to know how to deduce the last line from the first three?

Tonio

The question is:

Are these system specifications consistent? "The router can send packets to the edge system only if it supports the new address space. For the router to support the new address space it is necessary that the latest software release be installed. The router can send packets to the edge system if the latest software release is installed, The router does not support the new address space."

The answer is that it is consistant.

However I would like to know how to find that out using a truth table.

Or at least question 61, (which starts with "Steve would like ...") as that question is supposed to be figured out using a truth table.