Explore BrainMass
Share

translate into Propositional Logic form

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

I have 25 statements I'm supposed to translate into Propositional Logic form and these three are giving me some trouble. Do you think you could help?

e) Liza Minelli marries another businessman if Michael Jackson has another nose job, provided it is not the case that neither Britney Spears nor Justin Timberlake is videotaped being drunk in public.

I have this one set up so that:
L= Liza Minelli M=Michael Jackson
B=Britney Spears J=Justin Timberlake

f) Either Washington state repeals the death penalty or George Bush stages another made-for-tv campaign event unless Howard Dean adds another 5 million dollars to his campaign fund..

I have this one set up so that:
W=Washington G=George Bush H=Howard Dean

k) Ozone depletion is a necessary and sufficient condition for increased cancer rates if and only if the US's refusal to sign the Kyoto protocol is neither a necessary condition for Ozone depletion nor a sufficient condition for for increased cancer rates.

I have this one set up so that:
O=Ozone depletion I=increased cancer rates U=US's refusal to sign

© BrainMass Inc. brainmass.com October 24, 2018, 5:29 pm ad1c9bdddf
https://brainmass.com/philosophy/logic-critical-thinking/translate-into-propositional-logic-form-11713

Solution Preview

{I use "->" for implication; "~" for negation; "&" conjunction; "V" for disjunction; "<->" for bi-conditional. )
<br><br><br><br>
<br>
<br><br><br><br>e) Liza Minelli marries another businessman if Michael Jackson has another nose job, provided it is not the case that neither Britney Spears nor Justin Timberlake is videotaped being drunk in public.
<br><br><br><br>L = Liza Minelli marries another ...

Solution Summary

This job translates into Propositional Logic form. The sufficient conditions for increased cancer rates are analyzed.

$2.19
See Also This Related BrainMass Solution

Logic

Logic

1. Let p, q, and r be the following statements:
p: Roses are red
q: The sky is blue
r: The grass is green
Translate the following statements into English
(a) p &#61657; q (b) p &#61657; (q &#61658; r) (c) q &#61614; (p &#61657; r) (d) ( &#61566; r &#61657; &#61566; q) &#61614; &#61566; p

2. Write in symbolic form using p, q, r, &#61566;, &#61614;, &#61658;, &#61657;, where p, q, r represent the following statements:
p: A puppy is green-eyed
q: A puppy can be taught
r: A puppy loves toys

(a) If a puppy is green-eyed, then it cannot be taught
(b) If a puppy cannot be taught, then it does not love toys
(c) If a puppy loves toys, then either the puppy can be taught or the puppy is green-eyed.
(d) If the puppy is not green-eyed, then the puppy loves toys and the puppy can be taught.

3. Fill the headings of the following truth table using p, q, &#61566;, &#61614;, &#61658;, and &#61657;.

p q (a) (b)
T T T F
T F T F
F T T F
F F F T

4. For each of the following conditionals, identify the antecedent and the consequent. Form the converse, inverse, and contrapositive.

(a) If I don't go to the movie, I'll study my math.
(b) Your car won't start if you don't have gasoline in the tank.

5. Use De Morgan's laws to write an equivalent statement for the following sentence:
If we go to San Antonio, then we will go to Sea World or we will not go to Busch Gardens.

6. (a) Translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.

If Lillian passes the bar exam, then she will practice law.
Lillian will not practice law
----------------------------------------------------------------------
&#61532; Lillian did not pass the bar exam

7. Use an Euler diagram to determine whether the syllogism is valid or invalid
All actresses are beautiful
Some actresses are tall
--------------------------------
&#61532; Some beautiful people are tall.
8. Construct a truth table for (&#61566;q&#61657;p) &#61614; &#61566;q

View Full Posting Details