Help with Logic Questions! Forum

[BarnumOhio]

I'm trying to study for an upcoming exam and there are some questions I am having trouble with. If someone could help me with these I would really appreciate it!

Given that A, B, and C are true and X, Y and Z are false, determine the truth value of the following statements.

1. A v (B>Z) **> is the closest thing i could find to the backwards c thing**

2. ~B v ~X

3. (X>A) . (~B=Y)

4. [(A v B) . ~(Y>~C)] v~[~(Z>~X)v~B]

5. ~{~[~(A>~Y) . ~(Y>C)] v~ [~(B>~Z) . ~ (XvA)]}


Thanks!

[BarnumOhio]

Also if anyone knows somewhere else that could help, that'd be great!

[suspicious android]

#2 is true, since all you need to make a disjunction true is for either disjunct to be true, and ~X is true, since X is false.

Don't recognize the "backwards c" thing. What are you trying to make there?

[BarnumOhio]

It looks like a "U" with the mouth turned to the left. If that makes any sense haha. Thanks

[homestyle28]

OP means the conditional/implication sign

1. true. "v" or disjunction is true when either side (or both) is true

2. true. Same reason. ~X is true b/c X is false.

3 True. (if I'm understanding your symbols, is the right side the triple bar/equivalence symbol?). The "." is conjunction, true when both sides are true. Left side is true b/c it's a conditional w/ a false antecedent and the right side is true b/c both sides of the equivalence are false.

4. As you've typed it, it's not a well formed formula / valid sentence in symbolic logic. Your parentheses don't match up. Double check it.

5. False. The left most ~ is the main operator, it gets it's truth value from the v in the middle. The left side of that disjunct gets its value from the second left most ~. That ~ is true b/c it gets its value from the . between the 2 conditionals on the left. The first conditional is false, so the . is false, making the 2nd left most ~ true, making the V true.

FWIW I taught this at the college level for 2 years. feel free to ask more questions.

[homestyle28]

Also, is there any chance you're a student at Ohio U.?

[BarnumOhio]

I fixed number 4. Sorry for the mistake!

I do not go to OU, I go to Kent State.

Thanks again for all the help!

[homestyle28]

4 still looks a little off to me, it depends on where the ~ goes.

option 1: [(A v B) . ~[(Y>~C) v~[~(Z>~X)v~B]

False.

option 2:[(A v B) . [~(Y>~C)] v~[~(Z>~X)v~B]

False

Option 3: [(A v B) . [~(Y>~C) v~[~(Z>~X)v~B]

False

[BarnumOhio]

Alright there must be something wrong with the problem then, I will bring it up to my teacher.

There were two more questions that I was having problems with.

If you don't want to do them it's fine, you have already helped more than enough!

I need to determine the validity of the following argument:
~[A>(~B . X)]>~[(C v P) . ~(F>E)]
(C v P) . ~(F>E)
A>(~B . X)

Also I need to translate this statement into propositional logic form!

It is not the case that Mel Gibson is crazy if and only if it is not the case that if either Kyle or Stan liked the Passion, then Cartman is not president of the Mel Gibson fan club.

Thank you!

[homestyle28]

Alright there must be something wrong with the problem then, I will bring it up to my teacher.

There were two more questions that I was having problems with.

If you don't want to do them it's fine, you have already helped more than enough!

I need to determine the validity of the following argument:
~[A>(~B . X)]>~[(C v P) . ~(F>E)]
(C v P) . ~(F>E)
A>(~B . X)

Also I need to translate this statement into propositional logic form!

It is not the case that Mel Gibson is crazy if and only if it is not the case that if either Kyle or Stan liked the Passion, then Cartman is not president of the Mel Gibson fan club.

Thank you!

Good thing for you it's a slow day at work!

That argument is valid. I used both indirect truth tables and truth trees to check it.

~M <-> ~[(KvS) --> ~C]

M - MG is crazy
K - Kyle liked the passion
S - Stan liked the passion
C - Cartman is the president of the MG fan club

<-> - equivalence/triple bar symbol.
--> conditional arrow/horshoe

Also, as a former logic instructor, I would be remiss not to say that, in the long run, it's better for you to learn how to do this.

[BarnumOhio]

Alright there must be something wrong with the problem then, I will bring it up to my teacher.

There were two more questions that I was having problems with.

If you don't want to do them it's fine, you have already helped more than enough!

I need to determine the validity of the following argument:
~[A>(~B . X)]>~[(C v P) . ~(F>E)]
(C v P) . ~(F>E)
A>(~B . X)

Also I need to translate this statement into propositional logic form!

It is not the case that Mel Gibson is crazy if and only if it is not the case that if either Kyle or Stan liked the Passion, then Cartman is not president of the Mel Gibson fan club.

Thank you!

Good thing for you it's a slow day at work!

That argument is valid. I used both indirect truth tables and truth trees to check it.

~M <-> ~[(KvS) --> ~C]

M - MG is crazy
K - Kyle liked the passion
S - Stan liked the passion
C - Cartman is the president of the MG fan club

<-> - equivalence/triple bar symbol.
--> conditional arrow/horshoe

Also, as a former logic instructor, I would be remiss not to say that, in the long run, it's better for you to learn how to do this.

Completely understood. Thanks for including the steps on how you figured it out, I'm going to print this out and use it as a guide! Thanks again for all the help!