# Truth tables

1. Jan 20, 2007

### UrbanXrisis

1. The problem statement, all variables and given/known data

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

2. Relevant equations

none

3. The attempt at a solution

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

2. Jan 21, 2007

### theperthvan

3. Jan 21, 2007

### HallsofIvy

Staff Emeritus
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.

4. Jan 21, 2007

### 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"

5. Jan 21, 2007

### HallsofIvy

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

6. Jan 21, 2007

### 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
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)

7. Jan 21, 2007

### MeJennifer

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)".

Last edited: Jan 21, 2007