## Lukecrayonz one year ago If p is true, q is false, and r is false, what is the vaue of (p ^ ~q) ^ r

1. zepdrix

Then what is ~q? If q is false, then ~q is true, ya? :)

2. zepdrix

3. Lukecrayonz

I'm trying to help my friend with this but I honestly have never done this, I understand that it is TTF but what makes the final answer true or false?

4. Lukecrayonz

Such as the next question: if p is true, q is true, and r is true, then what is the value pf (p ^ ~q) ^ r, it would be true, false, true but what would the answer be? True because there are two truths and one false?

5. zepdrix

Umm well if you start in the brackets..$\large\rm (True\wedge True)\wedge False$True AND True gives us True. And requires that both be true in order to get a true result.$\large\rm (True)\wedge False$Again we have AND which is requiring BOTH to be true :O So we get a false as our final result since the requirement wasn't met.

6. Lukecrayonz

Hmm I was wondering what the brackets meant lol. So for the following question I posted: (true and not true) and true (True and false) would equal out to be false (false) and True would then be false?

7. Lukecrayonz

Why would the following question be (True ^ True) when there is a not symbol next to q?

8. zepdrix

Oh I guess I misread that :) lol. Good catch

9. zepdrix

(true AND false) AND true gave you (false) AND true which further gave you false yah that sounds right! :)

10. Lukecrayonz

Oh no @zepdrix D: right when I needed you most haha

11. zepdrix

Sorry I left another gal hangin :d gotta keep jumpin back n forth

12. Lukecrayonz

1: F 2: F Correct so far?

13. zepdrix

True table can be a little tricky. Just need to list every possible combination of true/false for the three letters.

14. zepdrix

Ummm, ya that sounds right :D

15. zepdrix

5 minutes? :p oh boy that doesn't give su much to work with lol

16. Lukecrayonz

So basically anytime there is a false such as ~true which would be false ^ (true) So the line would be False ^ True its always false since I guess the false would overpower the true? Lol

17. Lukecrayonz

And if the answer is False ^ False, the answer is False?

18. zepdrix

It's not so much that it "overpowers" it. It's the fact that AND is a very strict requirement. AND is asking the question "ARE BOTH OF THESE THINGS TRUE?"

19. zepdrix

Correct False AND False gives a False result because we need both True to end up with True.

20. zepdrix

False ^ True => False True ^ False => False False ^ False => False True ^ True => True