1. ## Logic exercises

1. Neither X nor Y, or both X and Y.
2. X and Y are equally false.
3. Yes
4. No
5. Yes
6. Yes

Are these correct answer, could someone check?
Thank you.

2. ## Re: Logic exercises

You have almost all of those wrong. Have you really studied this at all?

The original form of the first is $\left( {X \wedge \neg Y} \right) \vee \left( {\neg X \wedge Y} \right)$.
i.e. "Exactly one is true". Now negate that.

3. ## Re: Logic exercises

No, it's an appendix in a book, where these questions are thrown at you after about 5 pages of some superficial info. I guess it's more like a test then; maybe I'm just too bad at it. I guess I'd better pick up a book on logic then. Thanks for pointing out the mistakes.

4. ## Re: Logic exercises

Plato, so what do we get here? In the first?

Is it just: $\neg(X \wedge \neg Y) \vee \neg(\neg X \wedge Y)$ or $(\neg X \wedge Y) \vee ( X \wedge \neg Y)$, which is the same as the original statement?

5. ## Re: Logic exercises

2. X and Y are equally false.
3. No
4. No
5. Yes
6. No

6. ## Re: Logic exercises

Originally Posted by maxpancho
Plato, so what do we get here? In the first?

Is it just: $\neg(X \wedge \neg Y) \vee \neg(\neg X \wedge Y)$ or $(\neg X \wedge Y) \vee ( X \wedge \neg Y)$, which is the same as the original statement?
If you are confused, then please study this.

7. ## Re: Logic exercises

Ah okay. So we just invert the truth table and get the result. So in this case it turns out that by negating we get the truth table of iff.

Also, I can only write it like this $\neg((X \wedge \neg Y) \vee (\neg X \wedge Y))$ and not like I did.

So 1 and 2 are invert of each other pretty much.

8. ## Re: Logic exercises

And I actually I just checked on wolfram (hadn't known I could have looked up truth tables there) it turns out that in the original post the answer to 3-6 were correct?

Spoiler:

3. https://www.wolframalpha.com/input/?...plies+not+y%29
4. https://www.wolframalpha.com/input/?...plies+not+x%29
5. https://www.wolframalpha.com/input/?...+%28y+iff+z%29
6. https://www.wolframalpha.com/input/?...z+implies+x%29