How to write statements with negation and disjunction in symbolic form?

[UrbanXrisis]

Homework Statement

This is just a simple logic question that I need a little guidance.
Let X= "I like cars"
Let Y= "I like trees"
Let ~ = not
Let V = or

How would this be written in symbols:
1. It is not the case that I like cars or I like trees
2. It is not the case that I like cars, or I like trees

Homework Equations

none

The Attempt at a Solution

1. ~X V Y
2. ~(X V Y)

 

[theperthvan]

your answers should be vice versa I think

 

[HallsofIvy]

First statement: "It is not the case that: (I like cars or I like trees).

Second statement: (It is not the case that I like cars) or (it is not the case that I like trees).

I agree with theperthvan.

 

[UrbanXrisis]

that's what I thought, but the examples in the book gives the following:

P=Irene has red hair

PV~P = "Irene has red hair or she dos not have red hair"

if what you say is correct, then the example should say:

PV~P = "Irene has red hair, or she dos not have red hair"

 

[HallsofIvy]

?? The only difference I see is a comma which, grammatically, is optional here. Both sentences mean the same thing.

 

[UrbanXrisis]

then shouldn't this be the same thing as well?
1. It is not the case that I like cars or I like trees
2. It is not the case that I like cars, or I like trees

Say X- I like cars and Y=I like trees
then using the example from the book

PV~P = "Irene has red hair or she dos not have red hair"

i could say ~X V Y, which would read: "I do not like cars or I like trees"

looking back at
1. It is not the case that I like cars or I like trees

would this be ~X V Y and not ~(X V Y)

 

[MeJennifer]

Second statement: (It is not the case that I like cars) or (it is not the case that I like trees).

The statement: "It is not the case that I like cars, or I like trees" also could read "(It is not the case that I like cars) or (It is the case that I like trees)".