<< Chapter < Page Chapter >> Page >
Problems on propositional logic, including truth-tables, boolean algebra, and inference rules.

Please write logic formulas using the syntax previously defined , using (or for brevity,

F
), (or
T
), ¬, ∧, ∨, and ⇒.Except where directed, use only these connectives.

You can download WaterWorld if you like. At Rice University, WaterWorld is installed on OwlNet, in /home/comp280/bin/waterworld .

Propositional logic

[Practice problem solution provided.]

Your friend Tracy argues:

It is bad to be depressed. Watching the news makes me feel depressed.Thus, it's good to avoid watching the news.

Regardless of whether the premises and conclusion are true, show that the argument is not, by showing it doesn't hold for all domains.Replace

depressed
and
watching news
with expressions which leave the premises true,but the conclusion false (or at least, what most reasonable people would consider false).

Lots of possible counterexamples.

It is bad to be depressed. Doing homework makes me depressed;so it's good to not do my homework.
Or,
It is bad for people to be in physical pain. Childbirth causes pain.Therefore childbirth needs be avoided by all people.
If the original conclusion is really correct, Tracy needs to elucidate some of his unspoken assumptions.

The flaw seems to be along the lines of,

avoiding bad in the short run may not always be good in the long run
(or equivalently, sometimes you have to choose the lesser of two evils).No, you weren't asked to name a specific flaw, and reasonable people can differ on precisely what the flaw is.(And, formal logic is not particularly helpful here.) Nonetheless, uncovering hidden assumptionsin arguments often helps understand the real issues involved.

For fun, pick up the front page of the daily newspaper,and see how many arguments use faulty rules of inference and/or rely on unspoken premises (which not all might agree with).In particular, political issues as spun to the mainstream press are often riddled with error,even though there are usually reasonable arguments on both sides which policy-makers and courts debate.

Got questions? Get instant answers now!

[Practice problem solution provided.]

An acquaintance says the following to you:

Chris claims knowledge is more important than grades. But she spent yesterday doing an extra-credit assignmentwhich she already knew how to do. Therefore, she's a hypocrite and deserves no respect.

Regardless of whether the premises and conclusion are true,show that the argument is not, by showing it doesn't hold for all domains.Replace

knowledge
and
grades
with expressions which give you true premises, but a false conclusion(or at least, what most reasonable people would consider false).
Exaggerate
knowledge
to something more important, and
grades
to something less important.

Terry claims that encouraging human-rights is more important than playing Tetris.But Terry played Tetris yesterday rather than volunteering with Amnesty International .
Most people wouldn't condemn Terry as a hypocrite just because of this; even the most dedicated of people areentitled to some free time. If your friend wants to prove Terry hypocritical,they'll have to provide further evidence or arguments.

Or similarly,

Politician X claims to support science funding, but voted against a proposal to shift all Medicare funds to NASA.

Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Intro to logic. OpenStax CNX. Jan 29, 2008 Download for free at http://cnx.org/content/col10154/1.20
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Intro to logic' conversation and receive update notifications?

Ask