Prove this Tautology (No Truth Tables)

Posted by FSM on Super User See other posts from Super User or by FSM
Published on 2010-03-22T23:54:00Z Indexed on 2010/03/23 0:01 UTC
Read the original article Hit count: 738

Filed under:

logic

|

math

|

homework

This is for homework for my Discrete Math class.

I understand how to prove tautologies with a truth table. I'm having trouble figuring out how to do it without though.

I found this example in our text, but the solution is not provided. I was hoping someone could answer it as best they could so I could apply it to my other questions. Thanks!

! = not/invert
^ = and
V = or
-> = if then

[!P ^ (P V Q) ] -> Q

I also am completely lost for this question (I fear I'll be tested on something of this difficulty)

[ (P -> Q) ^ (Q -> R) ] -> (P -> R)

Thanks for the help all!

© Super User or respective owner

Related posts about logic

Business Logic Layer Pattern on Rails? MVCL

as seen on Stack Overflow - Search for 'Stack Overflow'
That is a broad question, and I appreciate no short/dumb asnwers like: "Oh that is the model job, this quest is retarded (period)" PROBLEM Where I work at people created a system over 2 years for managing the manufacture process over demand in the most simplified still broad as possible, involving… >>> More
What is the correct way to deal with similar but independent features?

as seen on Programmers - Search for 'Programmers'
Let's say we have a feature request come in and we begin work on it, which we'll call feature-1. It introduces some new logic to the application, which we'll call logic-A and logic-B. A programmer branches from the release branch and begins work on the feature. Soon after, we get another feature… >>> More
What is up with the Joy of Clojure 2nd edition?

as seen on Programmers - Search for 'Programmers'
Manning just released the second edition of the beloved Joy of Clojure book, and while I share that love I get the feeling that many of the examples are already outdated. In particular, in the chapter on optimization the recommended type-hinting seems not to be allowed by the compiler. I don't know… >>> More
Transforming Business Logic into Web Services Using DB2 9.5 and IBM Data Studio

as seen on Internet.com - Search for 'Internet.com'
Learn how to take business logic such as stored procedures, functions, or SQL statements and turn them into a Web service. >>> More
Identifier for the “completed” stage of a process: 0, 99, something else?

as seen on Programmers - Search for 'Programmers'
Say, that you are handling a multi-step process (like a complex registration form, with a number of steps the user has go through in order). You need to be able to save the current state of the process (e.g. so the user can come back to that registration form later and continue form the step where… >>> More

Related posts about math

how to make a function recursive

as seen on Stack Overflow - Search for 'Stack Overflow'
i have this huge function and i am wondering how to make it recursive. i have the base case which should never come true, so it should always go to else and keep calling itself with the variable t increases. any help would be great thanks def draw(x, y, t, planets): if 'Satellites' in planets["Moon"]: … >>> More
Sunrise / set calculations

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm trying to calculate the sunset / rise times using python based on the link provided below. My results done through excel and python do not match the real values. Any ideas on what I could be doing wrong? My Excel sheet can be found under .. http://transpotools.com/sun_time.xls # Created on… >>> More
Android-Java: Constructing a triangle based on Coordinates on a map and your bearing

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi Guys, I'm constructing a geolocation based application and I'm trying to figure out a way to make my application realise when a user is facing the direction of the given location (a particular long / lat co-ord). I've got the math figured, I just have the triangle to construct. //UPDATE So… >>> More
Math.max and Math.min outputting highest and lowest values allowed

as seen on Stack Overflow - Search for 'Stack Overflow'
so I'm trying to make a program that will output the sum, average, and smallest and largest values. I have everything basically figured out except the smallest and largest values are outputting 2147483647 and -2147483647, which I believe are the absolute smallest and largest values that Java will… >>> More
Is Programming == Math?

as seen on Stack Overflow - Search for 'Stack Overflow'
I've heard many times that all programming is really a subset of math. Some suggest that OO, at its roots, is mathematically based. I don't get the connection. Aside from some obvious examples: using induction to prove a recursive algorithm formal correctness proofs functional languages lambda calculus asymptotic… >>> More